Question

shelton earns an hourly wage at a grocery store. the following expression represents Sheltons take home pay after taxes, social security, and his health care plan deducted. let x represent the number of hours shelton worked. 10.25x-0.21(10.25x) part A: which term represents sheltons total pay before deduction. part B:which term represents sheltons deductions. part C:how much is sheltons hourly wage. part D:what percentage is decuted from sheltons pay for taxes , social security , and health care plan. part E: shelton wants to save 1675 for a new laptop. if shelton saves 25% of his take hime pay,how many hours will be need to work to meet his savings goal

Answer 1

The expression that represents Shelton's take-home pay after all deductions is:

`10.25x-0.21\mleft(10.25x\mright)`

(a)Shelton's total pay before deduction = $10.25x

(b) Shelton's deductions = $0.21(10.25x)

(c)Since x represents the number of hours Shelton worked, his hourly wage will be: $10.25

(d)Since 0.21 of his total pay is deducted, the percentage that is deducted from Shelton's pay is 21%.

(e)If Shelton saves 25% of his take-home pay, this will be:

`0.25(10.25x-0.21\mleft(10.25x\mright))`

If he wants to save $1,675, we then have:

`0.25(10.25x-0.21\mleft(10.25x\mright))=1675`

We are required to solve for x.

`\begin{gathered} 0.25(10.25x-2.1525x)=1675 \\ 0.25(10.25x-2.1525x)=1675 \\ 0.25*8.0975x=1675 \\ 2.024375x=1675 \\ x=(1675)/(2.024375) \\ x=827.4\approx827\text{ hours} \end{gathered}`

Shelton will work for 827 hours to meet his goal.