Regents Exam Questions A.CED.A.2 & A.CED.A.3 - Modeling Equations & Inequalities PDF

# Regents Exam Questions A.CED.A.2: Modeling Linear Equations ## Modeling Linear Equations **Name:** Answer key 1. The width of a rectangle is 4 less than half the length. If *l* represents the length, which equation could be used to find the width, *w*? 1. *w* = 2(4 - *l*) 2. *w* = 1/2(*...

# Regents Exam Questions A.CED.A.2: Modeling Linear Equations ## Modeling Linear Equations **Name:** Answer key 1. The width of a rectangle is 4 less than half the length. If *l* represents the length, which equation could be used to find the width, *w*? 1. *w* = 2(4 - *l*) 2. *w* = 1/2(*l* - 4) 3. *w* = 1/2*l* - 4 4. *w* = 4 - *l* 2. A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is $0.05 per megabyte. If *d* represents the number of additional megabytes used and *c* represents the total charges at the end of the month, which linear equation can be used to determine a user's monthly bill? 1. *c* = 60 - 0.05*d* 2. *c* = 60.05*d* 3. *c* = 60*d* - 0.05 4. *c* = 60 + 0.05*d* 3. A typical cell phone plan has a fixed base fee that includes a certain amount of data and an overage charge for data use beyond the plan. A cell phone plan charges a base fee of $62 and an overage charge of $30 per gigabyte of data that exceed 2 gigabytes. If *C* represents the cost and *g* represents the total number of gigabytes of data, which equation could represent this plan when more than 2 gigabytes are used? 1. *C* = 30 + 62(2 - *g*) 2. *C* = 30 + 62(*g* - 2) 3. *C* = 62 + 30(2*g*) 4. *C* = 62 + 30(*g* - 2) 4. The cost of one pound of grapes, *g*, is 15 cents more than one pound of apples, *a*. The cost of one pound of bananas, *b*, is twice as much as one pound of grapes. Write an equation that represents the cost of one pound of bananas in terms of the cost of one pound of apples. *b* = 2(*a* + 0.15) 5. The table below represents the number of hours a student worked and the amount of money the student earned. | Number of Hours (*h*) | Dollars Earned (*d*) | |---|---| | 8 | $50.00 | | 15 | $93.75 | | 19 | $118.75 | | 30 | $187.50 | Write an equation that represents the number of dollars, *d*, earned in terms of the number of hours, *h*, worked. Using this equation, determine the number of dollars the student would earn for working 40 hours. *d* = 6.25*h* *d* = 6.25(40) = 250 6. Sandy programmed a website's checkout process with an equation to calculate the amount customers will be charged when they download songs. The website offers a discount. If one song is bought at the full price of $1.29, then each additional song is $.99. State an equation that represents the cost, *C*, when *s* songs are downloaded. Sandy figured she would be charged $52.77 for 52 songs. Is this the correct amount? Justify your answer. *C* = 1.29 + .99(*s* - 1) No because *C* = 1.29 + .99(52 - 1) = 51.78 # Regents Exam Questions A.CED.A.3: Modeling Linear Inequalities ## Modeling Linear Inequalities **Name:** Answer key 1. An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of each DVD player (*d*) and a $30 profit on the sale of each cordless telephone (*c*). The store wants to make a profit of at least $255.00 from its sales of DVD players and cordless phones. Which inequality describes this situation? 1. 75*d* + 30*c* < 255 2. 75*d* + 30*c* ≤ 255 3. 75*d* + 30*c* > 255 4. 75*d* + 30*c* ≥ 255 2. Joy wants to buy strawberries and raspberries to bring to a party. Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. If she only has $10 to spend on berries, which inequality represents the situation where she buys *x* pounds of strawberries and *y* pounds of raspberries? 1. 1.60*x* + 1.75*y* ≤ 10 2. 1.60*x* + 1.75*y* ≥ 10 3. 1.75*x* + 1.60*y* ≤ 10 4. 1.75*x* + 1.60*y* ≥ 10 3. Peter has $100 to spend on drinks for his party. Bottles of lemonade cost $2 each, and juice boxes cost $0.50 each. If *x* is the number of bottles of lemonade and *y* is the number of juice boxes, which inequality models this situation? 1. 0.50*x* + 2*y* ≤ 100 2. 0.50*x* + 2*y* ≥ 100 3. 2*x* + 0.50*y* ≤ 100 4. 2*x* + 0.50*y* ≥ 100 4. David has two jobs. He earns $8 per hour babysitting his neighbor's children and he earns $11 per hour working at the coffee shop. Write an inequality to represent the number of hours, *x*, babysitting and the number of hours, *y*, working at the coffee shop that David will need to work to earn a minimum of $200. David worked 15 hours at the coffee shop. Use the inequality to find the number of full hours he must babysit to reach his goal of $200. 8*x* + 11*y* ≥ 200 → 8*x* + 11(15) ≥ 200 8*x* ≥ 35 *x* ≥ 4.375 **5 hours** 5. A school plans to have a fundraiser before basketball games selling shirts with their school logo. The school contacted two companies to find how much it would cost to have the shirts made. Company A charges a $50 set-up fee and $5 per shirt. Company B charges a $25 set-up fee and $6 per shirt. Write an equation for Company A that could be used to determine the total cost, *A*, when *x* shirts are ordered. Write a second equation for Company B that could be used to determine the total cost, *B*, when *x* shirts are ordered. Determine algebraically and state the minimum number of shirts that must be ordered for it to be cheaper to use Company A. *A*: 50 + 5*x* *B*: 6*x* + 25 5*x* + 50 < 6*x* + 25 50 < *x* + 25 25 < *x* **26 shirts** 6. The senior class at Hills High School is purchasing sports drinks and bottled water to sell at the school field day. At the local discount store, a case of sports drinks costs $15.79, and a case of bottled water costs $5.69. The senior class has $125 to spend on the drinks. If *x* represents the number of cases of sports drinks and *y* represents the number of cases of bottled water purchased, write an inequality that models this situation. Nine cases of bottled water are purchased for this year's field day. Use your inequality to determine algebraically the maximum number of full cases of sports drinks that can be purchased. Explain your answer. 15.79*x* + 5.69*y* ≤ 125 15.79*x* + 5.69(9) ≤ 125 15.79*x* ≤ 73.79 *x* ≤ 4.7 **Can buy 4 cases.**