Regents Exam Questions A.CED.A.2: Linear Equations

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Questions and Answers

Which inequality accurately models the profit scenario for the electronics store selling DVD players and cordless telephones?

75*d* + 30*c* < 255

75*d* + 30*c* > 255

75*d* + 30*c* ≥ 255 (correct)

75*d* + 30*c* ≤ 255

What inequality represents the situation where Joy can buy strawberries and raspberries with her budget of $10?

1.75*x* + 1.60*y* ≥ 10

1.75*x* + 1.60*y* ≤ 10

1.60*x* + 1.75*y* ≤ 10 (correct)

1.60*x* + 1.75*y* ≥ 10

For Peter's party drinks budget of $100, which inequality correctly represents the costs of lemonade and juice boxes?

0.50*x* + 2*y* ≤ 100

0.50*x* + 2*y* ≥ 100

2*x* + 0.50*y* ≥ 100

2*x* + 0.50*y* ≤ 100 (correct)

What is the minimum number of hours David must babysit to earn at least $200 given his other job?

5 hours Signup and view all the answers

Which equation represents the total cost for Company A if they charge a $50 setup fee and $5 per shirt?

A = 50 + 5x Signup and view all the answers

If Company B charges a $25 setup fee and $6 per shirt, which equation represents the total cost?

B = 25 + 6x Signup and view all the answers

Which of the following inequalities would NOT represent the ongoing budget constraint for purchasing goods?

2x + 0.50y = 100 Signup and view all the answers

What does the '≥' symbol in the inequality $8x + 11y ≥ 200$ signify?

David must earn at least $200 Signup and view all the answers

If the length of a rectangle is represented by l, what does the equation w = 1/2l - 4 describe?

The width is equal to half the length minus 4. Signup and view all the answers

Which linear equation correctly models the monthly bill for a user who pays $60 for 1 GB and $0.05 per additional MB?

c = 60 + 0.05d Signup and view all the answers

For a cell phone plan that charges a base fee of $62 and adds $30 for each GB beyond 2 GB, which equation represents the cost when more than 2 GB are used?

C = 62 + 30(g - 2) Signup and view all the answers

What is the relationship between the cost of bananas, grapes, and apples based on the equation b = 2(a + 0.15)?

Bananas cost twice as much as grapes. Signup and view all the answers

If a student earns $6.25 for each hour worked, which equation represents the total earnings based on hours worked, h?

d = 6.25h Signup and view all the answers

Using the equation d = 6.25h, what is the amount earned if a student works for 40 hours?

$250.00 Signup and view all the answers

What is the cost when downloading 52 songs, with the first song priced at $1.29 and each additional song at $0.99?

$52.77 Signup and view all the answers

In the equation w = 4 - l, what characteristic of the rectangle does this represent?

Width decreases as length increases. Signup and view all the answers

Study Notes

Regents Exam Questions A.CED.A.2: Modeling Linear Equations

Problem 1: If the width of a rectangle is 4 less than half the length (represented by 'l'), the equation for the width ('w') is w = (1/2)l - 4.
Problem 2: A cell phone company charges a base fee of $60 and $0.05 per megabyte of additional data. The total cost ('c') is found using the formula c = 60 + 0.05d, where 'd' is the number of additional megabytes used.
Problem 3: A cell phone plan has a base fee of $62 and an overage charge of $30 per gigabyte above 2 gigabytes. The cost ('C') is represented by C = 62 + 30(g - 2) when g > 2 represents gigabytes of data.
Problem 4: The cost of a pound of grapes (g) is 15 cents more than a pound of apples (a). The cost of a pound of bananas (b) is twice the cost of a pound of grapes. The equation is b = 2(a + 0.15).
Problem 5: A student's earnings are directly proportional to the number of hours worked (h). The equation is d = 6.25h. For 40 hours, earnings would be $250.

Regents Exam Questions A.CED.A.3: Modeling Linear Inequalities

Problem 1: A store wants a profit of at least $255 from selling 'd' DVD players and 'c' cordless phones. The profit on DVD players is $75 and on cordless phones is $30. The inequality is 75d + 30c ≥ 255.
Problem 2: Joy wants to spend $10 on strawberries (x pounds at $1.60/pound) and raspberries (y pounds at $1.75/pound). The inequality is 1.60x + 1.75y ≤ 10.
Problem 3: Peter has $100 to spend on lemonade (x bottles at $2/bottle) and juice boxes (y boxes at $0.50/box). The inequality is 2x + 0.50y ≤ 100.
Problem 4: David earns $8 per hour babysitting (x hours) and $11 per hour working at a coffee shop (y hours). He needs to earn at least $200. The inequality is 8x + 11y ≥ 200. If he works 15 hours at the coffee shop, the inequality 8x + 11(15) ≥ 200 finds that he needs at least 25.6 hours of babysitting
Problem 5: Two companies offer shirt printing: Company A charges a $50 set-up fee plus $5 per shirt (A = 50 + 5x); Company B charges a $25 set-up fee plus $6 per shirt (B = 25 + 6x). Determining the minimum number of shirts for Company A to be cheaper than Company B requires solving 50 + 5x < 25 + 6x, which answers at least 26 shirts.
Problem 6: The senior class has $125 to spend on sports drinks (15.79 per case x ) and bottled water ( 5.69 per case y ). Nine cases of bottled water are purchased. This leads to 15.79x + 5.69(9) ≤125 so the senior class can buy a maximum of 4 cases of sports drinks.

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Description

This quiz features a series of problems focused on modeling linear equations, designed to test your understanding of algebraic concepts. Each problem involves creating or interpreting equations based on real-world scenarios. Challenge your skills in recognizing and applying linear relationships!