Question

Jeffery babysits for 4 dollars per hour, he also works as a math tutor for 7 dollars per hour. He is only allowed to work 13 hours total per week. He wants to make at least 65 dollars. Write a system of inequalities to represent this situation.

Answer 1

Given:

Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.

He is only allowed to work 13 hours total per week.

He wants to make at least 65 dollars.

To find:

The system of inequalities to represent this situation.

Solution:

Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.

He is only allowed to work 13 hours total per week. It means sum of x and y must be less than or equal to 13.

`x+y\leq 13`

He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.

`4x+7y\geq 65`

Number of hours can not be negative.

`x\geq 0, y\geq 0`.

Therefore, the required system of inequalities contains some equations,
`x+y\leq 13,4x+7y\geq 65` and
`x, y\geq 0`.