NJGPA Creating and Solving Equations and Inequalities 3 — Questions and Answers
Question 1: An electrician charges $75 for the first hour and $50 for each additional hour. Which equation gives the total cost C for h hours (h > 1)?
- C = 75h
- C = 50h + 75
- C = 75 + 50(h − 1) (Correct answer)
- C = 125h − 50
Correct answer: C = 75 + 50(h − 1)
The first hour costs $75 and each additional hour (h − 1 hours) costs $50, so C = 75 + 50(h − 1).
Question 2: Solve for y: (y/3) + 5 = 11
- y = 2
- y = 12
- y = 18 (Correct answer)
- y = 48
Correct answer: y = 18
Subtract 5 to get y/3 = 6, then multiply both sides by 3: y = 18.
Question 3: The sum of three consecutive even integers is 54. What is the largest integer?
- 16
- 18
- 20 (Correct answer)
- 22
Correct answer: 20
Let the integers be n, n+2, n+4; then 3n + 6 = 54, n = 16, so the largest is 20.
Question 4: Which graph represents the solution set of −2 ≤ x < 4?
- Open circle at −2, closed circle at 4, shaded between
- Closed circle at −2, open circle at 4, shaded between (Correct answer)
- Closed circles at both −2 and 4, shaded between
- Open circles at both −2 and 4, shaded between
Correct answer: Closed circle at −2, open circle at 4, shaded between
≤ means a closed circle at −2, and < means an open circle at 4.
Question 5: A gym membership costs $40 to join and $30 per month. Kevin has $220 to spend. Which inequality shows the maximum number of months m he can afford?
- 30m + 40 ≤ 220 (Correct answer)
- 40m + 30 ≤ 220
- 30m − 40 ≤ 220
- 30m + 40 ≥ 220
Correct answer: 30m + 40 ≤ 220
Total cost is 30m + 40, and it must be at most $220, so 30m + 40 ≤ 220.
Question 6: Solve for x: |x − 3| = 7
- x = 4 only
- x = −4 only
- x = 10 or x = −4 (Correct answer)
- x = 4 or x = −10
Correct answer: x = 10 or x = −4
Setting x − 3 = 7 gives x = 10, and x − 3 = −7 gives x = −4.
Question 7: A truck can carry at most 2,000 pounds. Each crate weighs 150 pounds and the driver weighs 200 pounds. Which inequality gives the maximum number of crates c?
- 150c + 200 < 2000
- 150c + 200 ≤ 2000 (Correct answer)
- 150c ≤ 2000
- 200c + 150 ≤ 2000
Correct answer: 150c + 200 ≤ 2000
Total weight is 150c + 200, and it must not exceed 2,000: 150c + 200 ≤ 2000.
NJGPA Creating and Solving Equations and Inequalities 3
An electrician charges $75 for the first hour and $50 for each additional hour.
Which equation gives the total cost C for h hours (h > 1)?