Question

Karen earns $54.60 for working 6 hours. If the amount she earns varies directly with the

number of hours she works, how many hours would she need to work to earn an
additional $260?

Answer 1

Given:

Karen earns $54.60 for working 6 hours.

Amount she earns varies directly with the number of hours she works.

She need to work to earn an additional $260.

To find:

Number of hours she need to work to earn an additional $260.

Solution:

Let the amount of earnings be A and number of hours be t.

According to question,

`A\propto t`

`A=kt` ...(i)

where, k is constant of proportionality.

Karen earns $54.60 for working 6 hours.

`54.60=k(6)`

Divide both sides by 6.

`(54.60)/(6)=k`

`9.1=k`

Put k=9.1 in (i).

`A=9.1t`

Substitute A=260 in the above equation.

`260=9.1t`

Divide both sides by 9.1.

`(260)/(9.1)=t`

`28.5714=t`

`t\approx 29`

Therefore, she need to work extra about 29 hours to earn an additional $260.