Question

Carson is a high school student with two part-time jobs.He earns$6 per hour for baby sitting,and he earns $8 per hour doing clerical work for his father's business.His goal is to earn atleast $96 a week ,but because of school, he does not want to work more than 15 hours each week.

Answer 1

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Complete Question

Carson is a high school student with two part-time jobs. He earns $6 per hour for babysitting, and he earns $8 per hour doing clerical work for his father's business. His goal is to earn at least $96 a week, but because of school, he does not want to work more than 15 hours each week.  Let b represent the number of hours Carson works in one week at the babysitting job, and let c represent the number of hours Carson works in one week at his father's business. Which inequalities represent the constraints on what Carson can earn and the number of hours he can work in one week? Select all that apply.  

A) b+c≤15

B) 6b+8c≤15

C) 6b+8c≥15

D) b+c≥96

E) 6b+8c≥96

F) 6b+8c≤96

Answer:

A) b + c ≤ 15

E) 6b + 8c ≥ 96

Step-by-step explanation:

Let b represent the number of hours he can work babysitting

Let c represent the number of hours he can work clerical work

We can derive 2 inequality equations

From the question, we are told:

He does not want to work more than 15 hours each week because of school

This means the maximum he wants to work is 15 hours, meaning he can work less than that. So we used the inequality less than or equal to Hence:

b + c ≤ 15...... Equation 1

He earns$6 per hour for baby sitting,and he earns $8 per hour doing clerical work for his father's business.His goal is to earn atleast $96 a week.

This means $96 is the least amount he wants to earn , meaning he can earn more than that. So we used the inequality greater than or equal to

Hence:

$6 × b +$8 × c ≥ $96

6b + 8c ≥ 96

Therefore, the two inequalities that represent the constraints on what Carson can earn and the number of hours he can work in one week:

A) b + c ≤ 15

E) 6b + 8c ≥ 96