NJGPA Creating and Solving Equations and Inequalities 2 — Questions and Answers
Question 1: A cell phone plan charges a flat fee of $25 per month plus $0.10 per text message. If Maria's bill was $43, which equation can be used to find the number of text messages t she sent?
- 25t + 0.10 = 43
- 0.10t + 25 = 43 (Correct answer)
- 25 + 43t = 0.10
- 0.10 + 25t = 43
Correct answer: 0.10t + 25 = 43
The flat fee is $25 and each text costs $0.10, so 0.10t + 25 = 43.
Question 2: Solve for x: 3(2x − 4) = 18
- x = 3
- x = 5 (Correct answer)
- x = 7
- x = 9
Correct answer: x = 5
Distribute to get 6x − 12 = 18, then 6x = 30, so x = 5.
Question 3: Which inequality represents 'five more than twice a number n is at most 19'?
- 2n + 5 ≥ 19
- 2n − 5 ≤ 19
- 2n + 5 ≤ 19 (Correct answer)
- 5n + 2 ≤ 19
Correct answer: 2n + 5 ≤ 19
'At most' means less than or equal to, so 2n + 5 ≤ 19.
Question 4: A rectangle has a length that is 4 more than twice its width w. If the perimeter is 56, which equation models this situation?
- 2(2w + 4) = 56
- 2w + (2w + 4) = 56
- 2(w) + 2(2w + 4) = 56 (Correct answer)
- w + 2w + 4 = 56
Correct answer: 2(w) + 2(2w + 4) = 56
Perimeter = 2(width) + 2(length) = 2w + 2(2w + 4) = 56.
Question 5: Solve the inequality: −4x + 7 > 23
- x > −4
- x < −4 (Correct answer)
- x > 4
- x < 4
Correct answer: x < −4
Subtract 7 to get −4x > 16, then divide by −4 and flip the sign: x < −4.
Question 6: A store sells notebooks for $3 each and pens for $1.50 each. Carlos spent exactly $18 and bought twice as many pens as notebooks. How many notebooks did he buy?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
Let n = notebooks; pens = 2n. Then 3n + 1.50(2n) = 18 → 6n = 18 → n = 3.
Question 7: Which value of x satisfies both 2x + 1 > 5 and x − 3 < 2?
- x = 2
- x = 3 (Correct answer)
- x = 5
- x = 6
Correct answer: x = 3
From the first: x > 2; from the second: x < 5; x = 3 satisfies both.
NJGPA Creating and Solving Equations and Inequalities 2
A cell phone plan charges a flat fee of $25 per month plus $0.10 per text message.
If Maria's bill was $43, which equation can be used to find the number of text messages t she sent?