FREE NJGPA Creating and Solving Equations and Inequalities Questions and Answers

Question 1

A plumber charges a flat fee of $50 for a service call, plus $75 per hour of work. If a customer's total bill was $425, which equation could be used to find the number of hours, h, the plumber worked?

Accepted Answer

75h + 50 = 425

Answer

The total cost is the sum of the flat fee ($50) and the variable cost, which is the hourly rate ($75) multiplied by the number of hours (h). Therefore, the equation is 75h + 50 = 425.

Question 2

Maria is saving for a new laptop that costs $1,200. She has already saved $450. She earns $15 per hour at her part-time job. What is the minimum number of hours she must work to afford the laptop?

Accepted Answer

50 hours

Answer

Let h be the hours Maria works. Her earnings are 15h. Her total savings will be her current savings plus her earnings: 450 + 15h. She needs this amount to be at least $1,200. The inequality is 450 + 15h ≥ 1200. Solving for h gives h ≥ 50.

Question 3

A school sold 300 tickets for a play. Student tickets cost $5 each and adult tickets cost $8 each. If the school collected a total of $1,950, how many adult tickets were sold?

Accepted Answer

150

Answer

Let 's' be the number of student tickets and 'a' be the number of adult tickets. We have two equations: s + a = 300 and 5s + 8a = 1950. Solving the first for s (s = 300 - a) and substituting into the second gives 5(300 - a) + 8a = 1950, which simplifies to 1500 - 5a + 8a = 1950, then 3a = 450, so a = 150.

Question 4

Gym A charges a $100 membership fee plus $20 per month. Gym B charges a $50 membership fee plus $30 per month. After how many months will the total cost of both gyms be the same?

Accepted Answer

5 months

Answer

Set the cost expressions for both gyms equal to each other. Let 'm' be the number of months. The equation is 100 + 20m = 50 + 30m. Solving for m gives 50 = 10m, so m = 5.

Question 5

Kevin has a $50 gift card to an online music store. Each song costs $1.29. He must have at least $10 remaining on the card to keep the account active. What is the maximum number of songs he can buy?

Accepted Answer

31

Answer

Let 's' be the number of songs. The cost is 1.29s. The remaining balance is 50 - 1.29s. This amount must be greater than or equal to $10. The inequality is 50 - 1.29s ≥ 10. Solving gives 40 ≥ 1.29s, which means s ≤ 31.007. Since he can't buy a fraction of a song, the maximum is 31.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

FREE NJGPA Creating and Solving Equations and Inequalities Questions and Answers