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. Suppose Carson worked as a babysitter for 5 hours one week. What is the minimum number of full hours he would need to work at his father's business to earn at lease $96 that week?

Answer 1

Explanation:

Step one:

let the hours for babysitting be x

and the hours for doing clerical be y

we are told that Carson would like to earn $96 weekly

She babysits for $6 per hour

and earned $8 per hour doing clerical work

6x+8y=96---------------1

Carson cannot work more than a total of 15 hours per week

5x+y≤15-------------2

The system of equation for the situation is

6x+8y=96

5 x+y≤15

y=15-5 x

put y=15-5 x in eqn 1

6x+8(15-5 x)=96

6x+120-40x=96

collect like terms

6x-40x=96-120

-34x=-24

x=24/34

x=0.7

Approximately 1 hour babysitting

put x= 0.7 in 5x+y≤15

5(0.7)+y≤15

3.52+y≤15

y≤15-3.52

y=11.4

Approximately 11 hours doing clerical work

Answer 2

Explanation:

Step one:

let the hours for babysitting be x

and the hours for doing clerical be y

we are told that Carson would like to earn $96 weekly

She babysits for $6 per hour

and earned $8 per hour doing clerical work

6x+8y=96---------------1

Carson cannot work more than a total of 15 hours per week

5x+y≤15-------------2

The system of equation for the situation is

6x+8y=96

5 x+y≤15

y=15-5 x

put y=15-5 x in eqn 1

6x+8(15-5 x)=96

6x+120-40x=96

collect like terms

6x-40x=96-120

-34x=-24

x=24/34

x=0.7

Approximately 1 hour babysitting

put x= 0.7 in 5x+y≤15

5(0.7)+y≤15

3.52+y≤15

y≤15-3.52

y=11.4

Approximately 11 hours doing clerical work