Solve the following percentage math problems: 10. Last month, the prices of a single scoop ice cream and a double scoop ice cream were $20 and $38 respectively. Their prices are... Solve the following percentage math problems: 10. Last month, the prices of a single scoop ice cream and a double scoop ice cream were $20 and $38 respectively. Their prices are increased to $22 and $40 respectively this month. Which type of ice cream has a larger percentage increase in price? 11. The number of babies born in a city decreased from 5000 to 4000. Kitty claims that the percentage change in the number of babies born is -25%. Do you agree? Explain your answer. 12. The length of a metal rod is 25 cm. Its length is increased by 8% when heated. Find the increase in the length of the rod. 13. Yesterday, there were 420 cars in a car park. Today, the number of cars in the car park is increased by 30%. Find the number of cars in the car park today. 14. The speed of a car on a highway is 80 km/h. Its speed is decreased by 35% when it makes a turn. Find the speed of the car when making the turn. 15. The price of a painting is $3800 now. Find the new price of the painting if the percentage change in price is (a) +65%, (b) -22%. 16. The time taken to complete a project is 90 days. (a) If more manpower is added and the time taken is decreased by 20%, how many days will it take to complete the project now? (b) If an unexpected problem occurred and caused the time taken to be increased by 30%, how many more days are needed to complete the project? 17. The minimum height required for a child to play a certain game in a theme park is 110 cm. Thomas was 95 cm last year and he has grown taller by 20% over the past year. Can he play the game now? Explain your answer. 18. To enter a competition, athletes need to get a result of 24 s in at least one of the two trials of a 200 m run. In the first trial, Jacky ran 200 m in 25 s. In the second trial, Jacky reduced his time by 3%. Can Jacky enter the competition? Explain your answer. 19. The number of visitors to the botanical garden is increased by 60% to 24 000 this month. Find the number of visitors last month.
Understand the Problem
This appears to be percentage math problems from a textbook or worksheet, asking us to solve for percentage increases, decreases, and other related calculations. We will need to carefully read each question and determine the appropriate formula or approach to find the solution, sometimes questions may require multiple steps.
Answer
10. Single scoop 11. No, -20% 12. 2 cm 13. 546 14. 52 km/h 15. (a) $6270, (b) $2964 16. (a) 72 days, (b) 27 days 17. Yes, 114 cm > 110 cm 18. No, 24.25 s > 24 s 19. 15000
Answer for screen readers
- The single scoop ice cream has a larger percentage increase in price.
- No, the percentage change is -20%.
- The increase in the length of the rod is 2 cm.
- There are 546 cars in the car park today.
- The speed of the car when making the turn is 52 km/h.
- (a) The new price of the painting is $6270. (b) The new price of the painting is $2964.
- (a) It will take 72 days to complete the project now. (b) 27 more days are needed to complete the project.
- Yes, he can play the game because he is now 114 cm tall, which is taller than the minimum height of 110 cm.
- No, Jacky cannot enter the competition because the time in his second trial was 24.25 s, which is more than 24 s.
- The number of visitors last month was 15000.
Steps to Solve
- Question 10: Calculate the percentage increase for the single scoop ice cream
To find the percentage increase, we use the formula $Percentage Increase = \frac{New Value - Old Value}{Old Value} \times 100$. For the single scoop, the old price is $20 and the new price is $22. $Percentage Increase = \frac{22 - 20}{20} \times 100 = \frac{2}{20} \times 100 = 10%$
- Question 10: Calculate the percentage increase for the double scoop ice cream
For the double scoop, the old price is $38 and the new price is $40. $Percentage Increase = \frac{40 - 38}{38} \times 100 = \frac{2}{38} \times 100 \approx 5.26%$
- Question 10: Compare the percentage increases
Comparing the two percentage increases, $10% > 5.26%$. Therefore, the single scoop ice cream has a larger percentage increase in price.
- Question 11: Calculate the percentage change in the number of babies born
The number of babies decreased from 5000 to 4000. $Percentage Change = \frac{New Value - Old Value}{Old Value} \times 100 = \frac{4000 - 5000}{5000} \times 100 = \frac{-1000}{5000} \times 100 = -20%$
- Question 11: Evaluate Kitty's claim
Kitty claims the percentage change is -25%. Our calculation shows it to be -20%. Therefore, we do not agree with Kitty.
- Question 12: Calculate the increase in the length of the metal rod
The original length is 25 cm, and it increased by 8%. $Increase = 8% \times 25 = 0.08 \times 25 = 2$ cm
- Question 13: Calculate the number of cars in the car park today
The number of cars yesterday was 420, and it increased by 30%. $Increase = 30% \times 420 = 0.30 \times 420 = 126$ $Number of cars today = 420 + 126 = 546$
- Question 14: Calculate the speed of the car when making the turn
The original speed is 80 km/h, and it decreased by 35%. $Decrease = 35% \times 80 = 0.35 \times 80 = 28$ km/h $Speed when making the turn = 80 - 28 = 52$ km/h
- Question 15a: Calculate the new price of the painting with a +65% change
The original price is $3800, and it increased by 65%. $Increase = 65% \times 3800 = 0.65 \times 3800 = 2470$ $New price = 3800 + 2470 = 6270$
- Question 15b: Calculate the new price the painting with a -22% change
The original price is $3800, and it decreased by 22%. $Decrease = 22% \times 3800 = 0.22 \times 3800 = 836$ $New price = 3800 - 836 = 2964$
- Question 16a: Calculate the new time to complete the project with a 20% decrease
The original time is 90 days, and it decreased by 20%. $Decrease = 20% \times 90 = 0.20 \times 90 = 18$ days $New time = 90 - 18 = 72$ days
- Question 16b: Calculate the additional days needed with a 30% increase
The original time is 90 days, and it increased by 30%. $Increase = 30% \times 90 = 0.30 \times 90 = 27$ days $Additional days needed = 27$ days
- Question 17: Calculate Thomas's height this year
Thomas was 95 cm last year and grew by 20%. $Increase = 20% \times 95 = 0.20 \times 95 = 19$ cm $Thomas's height this year = 95 + 19 = 114$ cm
- Question 17: Determine if Thomas can play the game
The minimum height required is 110 cm, and Thomas is now 114 cm tall. Since $114 > 110$, Thomas can play the game.
- Question 18: Calculate Jacky's time in the second trial
Jacky ran 200 m in 25 s in the first trial and reduced his time by 3% in the second trial. $Reduction = 3% \times 25 = 0.03 \times 25 = 0.75$ s $Jacky's time in the second trial = 25 - 0.75 = 24.25$ s
- Question 18: Determine if Jacky can enter the competition
To enter, athletes need to get a result of 24 s or less in at least one trial. Jacky's time in the second trial is 24.25 s, which is greater than 24 s. Therefore, Jacky cannot enter the competition.
- Question 19: Calculate the number of visitors last month
The number of visitors increased by 60% to 24000 this month. Let $x$ be the number of visitors last month. $x + 60% \times x = 24000$ $x + 0.6x = 24000$ $1.6x = 24000$ $x = \frac{24000}{1.6} = 15000$
- The single scoop ice cream has a larger percentage increase in price.
- No, the percentage change is -20%.
- The increase in the length of the rod is 2 cm.
- There are 546 cars in the car park today.
- The speed of the car when making the turn is 52 km/h.
- (a) The new price of the painting is $6270. (b) The new price of the painting is $2964.
- (a) It will take 72 days to complete the project now. (b) 27 more days are needed to complete the project.
- Yes, he can play the game because he is now 114 cm tall, which is taller than the minimum height of 110 cm.
- No, Jacky cannot enter the competition because the time in his second trial was 24.25 s, which is more than 24 s.
- The number of visitors last month was 15000.
More Information
Percentage problems are frequently encountered in everyday life, such as calculating discounts, taxes, or understanding changes in quantities.
Tips
A common mistake is to calculate the percentage increase/decrease using the new value as the base instead of the original value. It's crucial to use the original value in the denominator of the percentage change formula. For example, in problem 10, computing the percentage as $(22-20)/22$ would lead to an incorrect answer.
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