Question

Diego has two jobs. He works 3 hours at the library each day, making $8 per hour. In addition, he works at a coffee shop, making $7.50 per hour. At the coffee shop, he works more than 4 hours but less than 7 hours

each day Diego needs to make at least $70 daily to afford his living expenses.
Which of the following systems represents the constraints given in this scenario?
Let I represent the number of hours he works at the library
and c represent the number of hours he works at the coffee shop.

A: l = 3
4 < c < 7
8l + 7.50 ≥ 70

B: l = 3
4 ≤ c ≤ 7
8l + 7.50 ≥ 70

C: 1 = 3
4 ≤ c ≤ 7
7.50l + 8c ≤ 70

D: 1=3
4 < c < 7
7.50l + 8c ≥ 70

Answer 1

• D. l = 3 || 4 < c < y || 8l + 7.5c ≥ 70

Explanation:

Work at library

• Time = 3 hours ⇒ l = 3
• Payment = $8 per hour
• Total payment = 8l

Work at coffee shop

• Time = between 4 and 7 hours ⇒ 4 < c < 7
• Payment = $7.5 per hour
• Total payment = 7.5c

Target income = at least $70 daily

So the system as per above parameters:

• l = 3
• 4 < c < y
• 8l + 7.5c ≥ 70

Correct option is D