Business Mathematics Reviewer PDF

Reviewer: Business Mathematics Examples and Solutions Examples and Solutions Examples and Solutions  Examples and Solutions How many one-fifths are there in 20? Examples and Solutions  Examples and Solutions Dave, Bea and Luis have 120,000 stock shares altogether. If 2/5 of the...

Reviewer: Business Mathematics Examples and Solutions Examples and Solutions Examples and Solutions  Examples and Solutions How many one-fifths are there in 20? Examples and Solutions  Examples and Solutions Dave, Bea and Luis have 120,000 stock shares altogether. If 2/5 of the shares are Dave’s and 38,000 of the remainder are Bea’s, how many stock shares does Luis have?  Examples and Solutions Rick spent 1/5 of his monthly salary on rent, 1/4 of the rest on food and saved the rest. If he saved ₱6,000 each month, how much was his monthly income? Examples and Solutions Examples and Solutions What is the difference between 39.99 and 25.01? Examples and Solutions What is 0.25 of 300? Examples and Solutions What is 250 divided by 0.05? Examples and Solutions Answer this: Answer this:  Examples and Solutions If gasoline costs ₱62.75 per liter and you purchase 10.5 liters, how much will you pay in total?  Examples and Solutions If the electricity rate is ₱9.56 per kilowatt-hour and you use 150.75 kWh in a month, what will your electricity bill be?  Examples and Solutions Mangoes are priced at ₱45.90 per kilogram. If you buy 2.25 kilograms, how much do you need to pay?  Examples and Solutions If your water rate is ₱18.35 per cubic meter and you consume 25.5 cubic meters, how much is your water bill?  Examples and Solutions How much is the price per kilogram of the chicken if you buy a 1.75 kilogram of chicken at a price of ₱289.63?  Answer Key: 1. ₱ 658.875 2. ₱ 1441.17 3. ₱103.28 4. ₱467.925 5. ₱165.50 Since we are dealing with money, round it off to the nearest hundredths 1. ₱ 658.88 2. ₱ 1441.17 3. ₱103.28 4. ₱467.93 5. ₱165.50  Example Lindsey made 400 tarts. She sold 60% of them in the morning and 0.25 of the remaining in the afternoon. After that, she gave away the rest to her relatives. How many tarts did she gave away?  Example John made 200 cupcakes. He sold 80% of them in the morning and 0.20 of the remaining in the afternoon. After that, He gave away the rest to his friends. How many cupcakes did he gave away? Example  Example John bought 40 fishes. He fried 1/4 of it then feed to his animals the 20% of the remaining fishes. What part of the whole of fishes he have left in percent? Example Example Example Example  Dennis balances 3 metal washers and 2 metal nuts on a balance scale. ✔ The ratio of the number of washers to washers nuts the number of nuts is 3:2. ✔ The ratio of the number of nuts to the number of washers is 2:3 A ratio is a comparison of two washers quantities that are expressed in the same unit of measure. nuts 1 In every classroom, there are 6 electric fans and 2 doors. What is the ratio of the number of electric fans to the number of doors? 3 ways in writing a ratio Word form six to two Colon form 6: 2 Fraction form 2 Mr. Santos earns ₱25,000 a month. He spends ₱20,000 and saves the rest. Find the ratio of his salary to savings. Salary ₱25,000 salary : savings - Expenses ₱20,000 ₱25,000 : ₱5,000 Savings ₱5,000 Fraction form Ratio form 5: 1 3 A proportion is an equality of two equal ratios. means 5 :2 = 10 : 4 extremes ? 2 x 10 = 5x4 ✔ 20 = 20 It is a proportion. 4 Is the ratio 6:7 equal to the ratio of 3:8? means 6 :7 = 3 :8 extremes ? 7x3 = 6x8 21 = 48 It is not a proportion. 5 Find the missing term in the proportion 5:7 = 10:n means 5 :7 = 10 : n extremes 5xn = 7 x 10 7 x 10 = 5 x n 70 = 5 x n 5 x n = 70 70 ÷ 5 = n n = 70 ÷ 5 n = 14 n = 14 6 Find the value of the missing term. TST (Time Saving Technique) 2x9 = 3xn 18= 3 x n n = 18 ÷ 3 n=2x3 n=6 n=6  Find the value of the missing term. TST (Time Saving Technique) TST (Time Saving Technique) To solve missing term in a proportion, make sure that product of the n=3x4 means is the same n=9x4 as the product of the n = 12 n = 36 extremes.  Unit rate is used to compare quantities in which the second quantity is one. ✔ To find the unit rate, divide the numerator by the denominator and express the answer in both units. 1 The cost of three erasable pens is ₱ 225. What is the unit rate? 75 ₱ 225 = 3 pcs 1 ₱ 75 per piece 2 Find the unit rate of a car that traveled 285 kilometers in 5 hours. 57 285 km = 57 km 5 hrs 1 hr 1 57 kilometers per hour 3 What is the unit rate of 2,700 tickets to 18 booklets? 150 2,700 tickets = 150 tickets 18 booklets 1 booklet 1 150 tickets per booklet  How much is the consumption rate 4 if your water bill amounted to ₱ 1,305 with 29 cubic meters used? 45 = 1 ₱ 45 per cubic meter 1 Chato and May shared rubber bands in a ratio of 7:3. If Chato has 49 rubber bands, how many rubber bands does May have? 2 The ratio of stock shares between Jacob and James is 7:10. Their combined shares worth ₱85,000. How much is the share of James? 3 Maria's sales is 7/8 as the sales of Nimfa. Nimfa's total sales is ₱64,000. What is the combined sales of Maria and Nimfa? 4 Kristine receives a monthly salary. She saves ₱5,000 every month and the rest are dedicated to expenses and emergency funds in the ratio of 7: 2. If the difference between the expenses and emergency funds is ₱15,000 how much is the monthly salary of Kristine? 5 Which of the following is the best buy? a. 50 kg of rice at ₱2,400 b. 25 kg of rice at ₱1,100 c. 10 kg of rice at ₱520 d. 5 kg of rice at ₱ 325 SUMMARY ✔ Unit rate is used to compare quantities in which the second quantity is one. ✔ To find the unit rate, divide the numerator by the denominator and express the answer in both units.  Kinds of Proportion  Direct Proportion 1 The ratio of pencils to erasers is 3 : 2. If there are 12 pencils, how many erasers are there? Step1: Step2: Set upfor Solve thethe ratios missing term pencils: erasers = pencils: means erasers 3xn = 2 x 12 3: 2 = 12 : erasers 3 x n = 24 3: 2 = 12 : n n = 24 ÷ 3 extremes n=8 There are 8 erasers. 2 Kelly and Sally share an amount of money. The ratio of their shares is 3:5. If Kelly has ₱900, how much is the money of Sally? Step1: Step2: Set upfor Solve thethe ratios missing term Kelly : Sally means = Kelly: Sally 3xn = 5 x 900 3: 5 = 900 : n 3 x n = 4,500 3: 5 = 900 : n n = 4,500 ÷ 3 extremes n = 1,500 Sally has ₱1,500.  Partitive Proportion A proportion describing the total amount being distributed into two or more unequal parts 3 Andres and Santi share a bag of 42 candies in the ratio of 4: 3. How many candies will each child receive? Andres Andres 4x6 42 Santi = 24 Santi 3x6 = 42 = 18 7 units = 42 Andres received 24 candies 1 unit = 42 ÷ 7 while Santi 18 received 1 unit = 6 candies. 4 Blu and Lyka share an amount of money in the ratio of 5:3. Blu has ₱8,000 more than Lyka. How much money do they share in all. 8,000 Blu 5 x 4,000 TST (Time Saving Technique) = 20,000 Total number of units Blu Lyka 3 x 4,000 =5+3=8 Lyka = 12,000 8 x 4,000 Total money = 8,000 = 32,000 20,000 + 12,000 2 units = 8,000 = 32,000 1 unit = 8,000 ÷ 2 Blu and Lyka shared ₱32,000 in all. 1 unit = 4,000 In indirect proportion, as one quantity increases the Indirect other quantity decreases proportionally. Also, as one Proportion quantity decreases the other quantity increases. 5 Bert has enough money for a 5 – days vacation if he spends ₱600 a day. For how many days will his money last if he decides to spend only ₱300 a day? Step2: Step1: Solve Set upfor thethe missing term ratios money : days = money: days 600 x 5 = 300 x n 600 5: 5==300 600: 300: :nn 3,000 = 300 x n n = 3,000 ÷ 300 n = 10 The money will last for 10 days. 5 Bert has enough money for a 1-week vacation if he spends ₱800 a day. For how many days will his money last if he decides to spend only ₱350 a day? 6 Ten builders can make a small house in 30 days. How long will it take 12 builders to do the same job at the same rate? Step1: Step2: Set upfor Solve thethe ratios missing term builders : days = builders: days 10 x 30 = 12 x n 10: :3030==12 10 12: :nn 300 = 12 x n n = 300 ÷ 12 n = 25 They can do the job in 25 days. 6 12 builders can make a small house in 3 months. How long will it take 20 builders to do the same job at the same rate?  Trade Discount The amount of discount that the wholesaler or retailer receives off the list price; the difference between the list price and the net price.  Net Price The price the manufacturer or retailer pays or the list price minus the trade discount.  Discount Rate It is the amount of item to be paid by the retailer to the manufacturer.  FORMULA Single Discount Rate Net Price Trade Discount NP= List Price – Trade Discount = Discount Rate x List Price NP = LP – TD or TD = DR x LP NP = LP – DR x LP NP = LP x (1 – DR) 1 An item listed at ₱10,000 is subject to a discount of 20%. What is the amount of discount and the net price? Given: LP = 10,000 DR = 20% Step 1 Find the trade Step 2 Find the net price discount NP = LP - TD TD = LP x DR NP = 10,000 – 2,000 TD = 10,000 x 20% NP= 8,000 = 10,000 x 0.20 TD = 2,000 The discount is ₱ 2,000 and the net price is ₱ 8,000. 2 The NPD Factory sold ₱20,000 worth of clothes to the KYG Store. The given amount represents the retail price of the clothes for which the NPD Factory has offered a 15% trade discount. What is the actual amount paid by KYG Store? What is the trade discount? Given: LP = 20,000 DR = 15% NP = ? TD = ? Step 1 Find the net price Step 2 Find the trade discount NP = LP x (1 – DR) TD = LP - NP NP = 20,000 x (1 - 15%) TD = 20,000 – 17,000 = 20,000 x 85% TD= 3,000 = 20,000 x 0.85 NP = 17,000 The amount paid by KYG store is ₱ 17,000 and the trade discount is ₱ 3,000. 3 What is the discount rate if the net price of an item is ₱7,500 after giving a discount of ₱2,500? Given: NP = 7,500 TD = 2,500 LP = ? DR = ? Step 1 Find the list price Step 2 Find the discount rate LP = NP + TD LP = 7,500 + 2,500 LP = 10,000 The discount rate is 25%  Summary ❑ Trade Discount = List Price x Discount Rate ❑ Net Price = List Price – Trade Discount TRADE DISCOUNT SERIES Reasons for using discount series: To encourage volume purchases To promote special or seasonal items To entice new clients Trade Discount Series/ Chain Discount The single equivalent rate of discount is not simply the sum of the individual discounts. 1 A manufacturer offers a refrigerator of ₱ 25,000, less trade discounts of 30%, 20% and 10%. What is the net price? How much is the trade discount? What single trade discount is equivalent to these series of discount? Step 4 1 2 3 5 Compute for thethe nettrade price discount single applying the trade rate of trade discount of 10% discount 30% 20% 17,500 NP 14,000 Given: LP = 25,000 TD 20% DR == 12,400 30% NP = ? 10% 12,600 NP = LP x ( 1 – DR) NP TD = LP NP == LP x ( LP –x NP 14,000 1 – DR) ( 1x–( DR) 1 – 10%) NP TD = 17,500 NP == 25,000 x ( 1 25,000 –x 12,600 14,000 – 20%) ( 1 – 30%) 90% NP TD = 17,500 NP == 12,400 x 25,000 x 70% 12,600 80% NP The = 14,000 NP =traded 17,500 net discount price is ₱ 12,400. is ₱ 12,600  Summary Net Price in a Series of Discounts NP = LP (1-DR1) (1-DR2) (1-DR3)… (1-DRN) Single Trade Discount Rate Equivalent STDRE = 1 – (1-DR1) (1-DR2) (1-DR3)… (1-DRN) A manufacturer offers a refrigerator of ₱ 25,000, less trade discounts of 30%, 20% and 10%. What is the net price. What single trade discount equivalent to these series of discount? What is the net single trade discount equivalent? price? Given: DR LP 1==30%, 25,000DR DR = 21 20% , =30%, DR DR =10% 32= 20% , DR3=10% STDRE NP = LP=(1-DR 1 – (1-DR 1 ) ) (1-DR 1 2 (1-DR ) ) (1-DR 2 3 (1-DR )… )… (1-DR 3 (1-DR N ) N ) STDRE = 1 –(1-30%) NP = 25,000 (1-30%)(1-20%) (1-20%)(1-10%) (1-10%) STDRE = 1 –(70%) NP = 25,000 (70%)(80%) (80%)(90%) (90%) STDRE = 49.6% NP = 12,600 The single trade net price is ₱discount 12,600 equivalent is 49.6% 2 A new model of cellphone is ₱ 40,500, subject to 15%, 20%, and 5% discounts. a. What is single rate equivalent? Given: LP = 40,500 DR1 =15%, DR2= 20% , DR3=5% STDRE = 1- (1-DR1) (1-DR2) (1-DR3)… (1-DRN) STDRE = 1- (1-15%) (1-20%) (1-5%) STDRE = 1- (85%) (80%) (95%) STDRE = 35.4% The single rate equivalent is 35.4% 2 A new model of cellphone is ₱ 40,500, subject to 15%, 20%, and 5% discounts. b. What is the net price? Given: LP = 40,500 STDRE = 35.4% = DR NP = LP(1 – DR) NP = 40,500(1 – 35.4%) NP = 26,163 The net price is ₱ 26,163. 2 A new model of cellphone is ₱ 40,500, subject to 15%, 20%, and 5% discounts. c. What is the trade discount? Given: LP = 40,500 NP = 26,163 TD = LP - NP TD = 40,500 – 26,163 TD = 14,337 The trade discount is ₱ 14,337.  Summary Net Price in a Series of Discounts NP = LP (1-DR1) (1-DR2) (1-DR3)… (1-DRN) Single Trade Discount Rate Equivalent STDRE = 1 – (1-DR1) (1-DR2) (1-DR3)… (1-DRN) ✔ Interest is a fee paid for borrowing money ✔ Simple interest simplifies interest calculations based on deposit or loan principal. Is = Prt Is = simple interest P = principal r = rate of interest t = time 1 Simple Interest Miguel invested ₱80,000 in a savings account that offers a 2.5% annual simple interest rate. How much interest will he earn after 3 years? What is the future value? Given: P = ₱80,000.00 ; r = 2.5% ; t = 3 years Is = Prt FV = P + Is Is = 80000 x 2.5% x 3 FV = 80000 + 6000 Is = 6000 FV = 86,000 The interest is ₱6,000.00, and the future value is ₱86,000.00 2 Simple Interest Kendrick decided to invest some money in a time deposit account that offers a 4% annual interest rate. After leaving his money untouched for 4 years, he found that the interest earned was ₱64,000. How much money did Juan originally invest? Kendrick deposited ₱400,000. 3 Simple Interest Ricky borrowed ₱25,000.00 and paid ₱1,250.00 interest for 6 months. What was the rate of interest? The rate of interest was 10%. COMPOUND INTEREST is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods. Conversion period (m) – the number of times in a year the interest will be compounded in a year The following are the common conversion periods in a year: annually : m = 1 semi-annually: m = 2 quarterly: m = 4 monthly : m = 12 4 Compound Interest Find the compound amount and interest earned on ₱15,000.00 for 1 year at 7% compounded semi-annually Solution: Given: P = ₱15,000.00 t = 1 year r = 7% m=2 Therefore, the future value is ₱16,068.38 and the interest is ₱1,068.38 FORMULA Simple & Compound Interests  Compound Interest 5 Pepe invested ₱500,000 in a savings account with a 2.5% annual interest rate compounded quarterly. How much will his investment be worth after 3 years, and how much interest will he earn during this time? Solution: Given: P = ₱500,000.00 t = 3 yrs r = 2.5% m=4 Therefore, the future value is ₱538,816.30 and the interest is ₱38,816.30 6 Compound Interest  i n o l og i es Markup, Markon and Markdown Te rm Cost refers to the amount spent by the person or group who is putting up the business. Retail price refers to the selling price or the amount for which a merchandise is sold in the market. Markup is the amount that a retailer adds on to the cost in order to gain profit.  ul a Markup, Markon and Markdown F o r m Retail Price = Cost + Markup 1 Frank sells a shirt for ₱200 with a markup of ₱40. What is the cost of producing one shirt? Given: Retail Price = ₱200 Markup = ₱40 Cost = Retail Price - Markup Cost = 200 – 40 Cost = 160 The cost of a shirt is ₱160.00  Markup, Markon and Markdown Based on Markup k u p cost = Percent of Markup x Cost a r M Based on the Markup = Percent of Markup x Retail Price retail price  Markup, Markon and Markdown 2 A stuffed toy cost ₱250 to manufacture and is marked up 60% based on cost. What is the retail price of the stuffed toy? Given: Cost = ₱250 Percent Markup = 60% Step 1 Step 2 Markup = Percent Markup x cost Retail Price = Cost + Markup Markup = 60% x 250 Retail Price = 250 + 150 Markup = 150 Retail Price = 400 The retail price is ₱400.  Markup, Markon and Markdown 3 What is the percent of mark up of Dennis’ shirt based on cost if he sells it for ₱500 with a markup of ₱100? Given: Retail Price = ₱500 Markup = ₱100 Step 1 Step 2 Cost = Retail Price - Markup Cost = 500 – 100 Cost = 400 Percent of Markup = 25% The markup is 25%.  Markup, Markon and Markdown 4 Grace got a bag at a cost of ₱2,400 and wants to sell it at 40% markup based on retail price. How much will she sell the bag for? Given: Cost = ₱2400 Markup = 40% RP Retail Price = Cost + Markup 60% Retail Price = 2400 100%Retail Price = 2400 + 40%of Retail Price 60% 60% 60% Re = 2400 Retail Price = 4000 The retail price is ₱4,000  ul a Markup, Markon and Markdown Fo r m Gross Profit Margin = Sale Price - Unit Cost Markon is a small amount added to the retail price for specific purpose  Markup, Markon and Markdown 5 If a product with a selling price of ₱62.50 has a markup of 25%, then we have as follows: Cost of Product Gross Profit Margin % Profit Margin = ₱ 50.00 = ₱ 12.50 = 20%  i no l o g i es Markup, Markon and Markdown Te rm Markdown is an amount reduced from the original selling price Trade discount is an amount marked down from the retail price  Markup, Markon and Markdown 6 A hoodie that has a list price of ₱800 is on sale for 35% off. What is the sale price of the hoodie? Given: List Price = ₱800 % of Markdown = 35% Step 1 Step 2 Markdown = List Price x % of Markdown Sale Price = List Price - Markdown Markdown = 800 x 35% Sale Price = 800 – 280 Markdown = ₱280 Sale Price = ₱520 The sale price of a hoodie is ₱520.  Markup, Markon and Markdown 7 A bicycle is originally sold for ₱5,600 and is marked down to sell for ₱3,920. Determine the markdown and the markdown rate. Given: Original Price = ₱5,600 Sale Price = ₱3,920 Sale Price = Original Price - Markdown 3,920 = 5,600 - Markdown Markdown = 5,600 – 3,920 Markdown = ₱1,680 % of Markdown = 30% The markdown is ₱1,680 and markdown rate is 30%  FORMULA 1 JM has a fruit stand in Davao City that sells grapes. He ordered 25 kg of grapes at ₱ 105 per kilogram. JM expects that 30% of the grapes will spoil after 3 days and cannot be sold. He wants a 25% markup based on his cost. What should JM price his grapes so he can achieve his target markup?  JM has a fruit stand in Davao City that sells grapes. He ordered 25 kg of grapes at ₱ 105 1 per kilogram. JM expects that 30% of the grapes will spoil after 3 days and cannot be sold. He wants a 25% markup based on his cost. What should JM price his grapes so he can achieve his target markup? Given: Spoilage Production = 25 kg = Production x Spoilage Rate Cost = 105 = 25 x 30% Spoilage rate = 30% = 7.5 Mark up rate = 25% Initial Selling Price = Cost x (100% + Mark Up Rate) = 105 x (100% + 25%) = 105 x 125% = 131.25 1 JM has a fruit stand in Davao City that sells oranges. He ordered 25 kg of grapes at ₱ 105 per kilogram. JM expects that 30% of the grapes will spoil after 3 days and cannot be sold. He wants a 25% markup based on his cost. What should JM price his grapes so he can achieve his target markup? Given: Production = 25 kg Cost = 105 Spoilage rate = 30% Mark up rate = 25% Total Target Sales = Production x Initial Selling Price = 25 x 131.25 = 3281.25 2 Fe owns a company that manufactures batteries. Based on the report of past productions, 8% of the batteries made are defective and cannot be sold. Fe's production team made 9 500 batteries. It costs ₱ 14 to produce one battery. If Fe wants a 35% markup on selling price (margin), what should Fe price each battery to make her target markup? 2 Fe owns a company that manufactures batteries. Based on the report of past productions, 8% of the batteries made are defective and cannot be sold. Fe's production team made 9 500 batteries. It costs ₱ 14 to produce one battery. If Fe wants a 35% markup on selling price (margin), what should Fe price each battery to make her target markup? Given: Rate Amount Production = 9500 Cost 65% 14 Cost = 14 Spoilage rate = 8% Markup 35% Mark up rate = 35% Selling Price 100% ?  Fe owns a company that manufactures batteries. Based on the report of past 2 productions, 8% of the batteries made are defective and cannot be sold. Fe's production team made 9 500 batteries. It costs ₱ 14 to produce one battery. If Fe wants a 35% markup on selling price (margin), what should Fe price each battery to make her target markup? Given: Spoilage Production = 9500 Cost = 14 = Production x Spoilage Rate Spoilage rate = 8% = 9500 x 8% Mark up rate = 35% = 760 Total Target Sales = Production x Initial Selling Price = 9500 x 21.54 = 204,630  Fe owns a company that manufactures batteries. Based on the report of past productions, 8% of 2 the batteries made are defective and cannot be sold. Fe's production team made 9 500 batteries. It costs ₱ 14 to produce one battery. If Fe wants a 35% markup on selling price (margin), what should Fe price each battery to make her target markup? Given: Production = 9500 Cost = 14 Spoilage rate = 8% Mark up rate = 35%  SUMMARY 1 Fernan grows bananas in his backyard. This month, he was able to harvest 240 kg of ripe bananas. He calculated his cost of production and found that it cost him around ₱ 10.25 to grow one kilogram of bananas. He also anticipated that 40% of his harvest will rot and cannot be sold. If Fernan wants a 90% markup based on his cost, how much should he price the bananas per kilogram?  Fernan grows bananas in his backyard. This month, he was able to harvest 240 1 kg of ripe bananas. He calculated his cost of production and found that it cost him around ₱ 10.25 to grow one kilogram of bananas. He also anticipated that 40% of his harvest will rot and cannot be sold. If Fernan wants a 90% markup based on his cost, how much should he price the bananas per kilogram? Given: Spoilage Production = 240 = Production x Spoilage Rate Cost = 10.25 Spoilage rate = 40% = 240 x 40% Mark up rate = 95% = 96 Initial Selling Price = Cost x (100% + Mark Up Rate) = 10.25 x (100% + 90%) = 10.25 x 190% = 19.48 1 Fernan grows bananas in his backyard. This month, he was able to harvest 240 kg of ripe bananas. He calculated his cost of production and found that it cost him around ₱ 10.25 to grow one kilogram of bananas. He also anticipated that 40% of his harvest will rot and cannot be sold. If Fernan wants a 90% markup based on his cost, how much should he price the bananas per kilogram? Given: Production = 240 Cost = 10.25 Spoilage rate = 40% Mark up rate = 95% Spoilage = 96 Initial Selling Price = 19.48 Total Target Sales = Production x Initial Selling Price = 240 x 19.48 = 4675.20 2 Gener breeds chicken in his vacant lot in Dumaguete. He ordered 800 heads of chicks and raised them. It costs him ₱ 6.50 to buy one head plus around ₱ 68 per head to raise them. He expects that 10% of the chicks will die. He wants a 15% markup based on cost. How much should he sell one full-grown chicken to be able realize his target margin? 2 Gener breeds chicken in his vacant lot in Dumaguete. He ordered 800 heads of chicks and raised them. It costs him ₱ 6.50 to buy one head plus around ₱ 68 per head to raise them. He expects that 10% of the chicks will die. He wants a 15% markup based on cost. How much should he sell one full-grown chicken to be able realize his target markup? Given: Spoilage Production = 800 = Production x Spoilage Rate Cost = 6.50 + 68 = 74.50 = 800 x 10% Spoilage rate = 10% = 80 Mark up rate = 15% 2 Gener breeds chicken in his vacant lot in Dumaguete. He ordered 800 heads of chicks and raised them. It costs him ₱ 6.50 to buy one head plus around ₱ 68 per head to raise them. He expects that 10% of the chicks will die. He wants a 15% markup based on cost. How much should he sell one full-grown chicken to be able realize his target markup? Given: Production = 800 Cost = 6.50 + 68 = 74.50 Spoilage rate = 10% Mark up rate = 15% Spoilage = 80 Initial Selling Price =87.65 Total Target Sales = Production x Initial Selling Price = 800 x 87.65 =70120 3 Unit Target Production Spoilage Unit Cost Markup Rate Selling Price of Perishable s ₱ 42.50 64% based 1,400 12% on cost ₱ 640 130% based 8,500 6% on cost ₱ 164 25% based 250 15% on selling price 4 Regina buys 300 kilos of tomatoes to sell in a wet market. Tomatoes are bought at ₱28 per kilogram. Regina wants at least 45% markup based on cost. If she knows that 30% of the tomatoes will rot and cannot be sold, what should be the selling price of her tomatoes per kilogram? 4 Regina buys 300 kilos of tomatoes to sell in a wet market. Tomatoes are bought at ₱28 per kilogram. Regina wants at least 45% markup based on cost. If she knows that 30% of the tomatoes will rot and cannot be sold, what should be the selling price of her tomatoes per kilogram? Given: Production = 300 Cost = 28 Spoilage rate = 30% Mark up rate = 45% 5 It costs Liza ₱ 2 925 to bake 150 pieces of cupcakes. She will use 20% of her production for "free taste" to her target customers. However, she doesn't want to incur further expenses so she will set the selling price higher to cover the cupcakes consumed during the free taste. If she is targeting a 60%, markup based on cost, how much should she sell each cupcake? 5 It costs Liza ₱ 2 925 to bake 150 pieces of cupcakes. She will use 20% of her production for "free taste" to her target customers. However, she doesn't want to incur further expenses so she will set the selling price higher to cover the cupcakes consumed during the free taste. If she is targeting a 60%, markup based on cost, how much should she sell each cupcake? 6 Bryan spends around ₱ 57.60 to make one box of macapuno balls. He was able to make 80 boxes of macapuno and wants to earn 35% margin. He expects that 10% of his production will expire and cannot be sold. How much should he sell each box of macapuno to be able to achieve the target margin? 6 Bryan spends around ₱ 57.60 to make one box of macapuno balls. He was able to make 80 boxes of macapuno and wants to earn 35% margin. He expects that 10% of his production will expire and cannot be sold. How much should he sell each box of macapuno to be able to achieve the target margin? Given: Production = 80 Cost = 57.60 Spoilage rate = 10% Mark up rate = 35% Rate Amount Cost 65% 57.60 Markup 35% Selling 100% ? Price Break-Even Point (BEP) Formula P(X) = F + V(X) where: P = price per unit X = volume of output (in units) F = fixed costs V = variable costs per unit Break-Even Point (BEP) Formula P(X) = F + V(X) REVENUE = TOTAL COSTS  PROFIT REVENUE > TOTAL COST BREAK - EVEN REVENUE = TOTAL COST LOSS REVENUE < TOTAL COST Break-Even Point (BEP) in Units 1 Rey owns a burger stand. The cost for making a burger is ₱7.00 and he sells it for ₱12.00. If his fixed cost per month is ₱10,000.00, how many burger must be sold to reach the break – even point? Given P = ₱12.00 V = ₱7.00 F = ₱10,000.00 X=?  Revenue = Total Cost P(X) = F + V(X) ₱12(2,000) = ₱10,000 + ₱7(2,000) ₱24,000 = ₱10,000 + ₱14,000 ₱24,000 = ₱24,000 2 Gerry owns a lemonade stand. It costs him ₱2.00 to make a glass of lemonade and sells it for ₱10.00. If his fixed cost per month is ₱12,000.00, Atleast how many glasses of lemonade must be sold to gain profit? Given P = ₱10.00 V = ₱2.00 F = ₱12,000 x=? 1,500 glasses of lemonade must be sold. 3 Maggie owns a florist shop. She buys each bunch of flowers for ₱149 and special wrapping paper for ₱300 per roll. Each roll of wrapping paper will wrap 300 bunches of flowers. Rent of her premises is ₱10,500 per month and she pays monthly insurance of ₱2,000. Maggie sells each bunch of flowers for ₱250. What is the break even point? So: Given: P = ₱ 250 P = ₱ 250 V = ₱ 150 Fixed Costs F = ₱ 12,500 Variable Costs = Rent ₱ 10,500 Flowers ₱ 149 Insurance ₱ 2,000 Paper ₱ 1 (₱300/300) Total FC ₱ 12,500 Total V ₱ 150 3 Maggie owns a florist shop. She buys each bunch of flowers for ₱149 and special wrapping paper for ₱300 per roll. Each roll of wrapping paper will wrap 300 bunches of flowers. Rent of her premises is ₱10,500 per month and she pays monthly insurance of ₱2,000. Maggie sells each bunch of flowers for ₱250. What is the break even point? Given: Fixed Costs P = ₱ 250 Variable Costs Rent = ₱ 10,500 Flowers So: Insurance ₱ ₱2,000 149 Paper PFC Total = ₱ 250 ₱ 1 (₱300/300) ₱ 12,500 Total V =V₱ 150 ₱ 150 F = ₱ 12,500