Question

Sylvia earns $7 per hour at her after school job. After working one week, she received a paycheck for $91.

a. Write and solve an equation to find the number of hours Sylvia worked to earn $91.

b. The greatest number of hours Sylvia can work in any week is 15. Write an inequality to represent this statement.

c. What is the greatest amount of money Sylvia can earn in one week?

please help

Answer 1

a.)
`hours=13`

b.)
`h\leq 15`

c.) $
`$105`

Explanation:

a.) If she earns $7 'per' hour, this multiplication. After a week, we need to see how many hours she worked to earn $91, so this goes behind the equal sign. Let h be the unknown number of hours:

`7h=91`

Solve for h. Divide both sides by 7:

`(7h)/(7)=(91)/(7)\\\\h=13`

Sylvia worked 13 hours at a rate of $7 an hour.

b.) She can work at most 15 hours a week. At 'most' can also mean less than or equal to. Let h be hours:

`h\leq 15`

Sylvia can work less than or equal to 15 hours per week.

c.) If Sylvia can work 15 hours, plug in this value for h into an equation when she earns $7 per hour. Let the product of the hours and money equal t for total:

`t=7(15)\\t=105`

The most money Sylvia can earn in a week is $105.

Finito.