Question

Kelly price sells college textbooks on commission. She gets 8 % on the first $7500 of​ sales, 16% on the next $7500 of​ sales, and 20% on sales over $ 15,000. In July of 1997 ​$9500, ShelbyShelby​'s sales total was

What was ShelbyShelby​'s gross commission for July​ 1997?

Answer 1

The commission would be $ 920.

Explanation:

Given,

Sales in 1997 ​= $ 9500,

Since, there is a commision of 8 % on the first $ 7500 of​ sales, 16% on the next $ 7500 of​ sales, and 20% on sales over $ 15,000,

If x represents the total sales,

Commission for x ≤ 7500 = 8% of x = 0.08x,

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of (x-7500)

= 600 + 0.16(x-7500),

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of 7500 + 20% of (x-15000)

= 600 + 1200 + 0.20(x-15000)

= 1800 + 0.20(x-15000)

Thus, the function that shows the given situation,

`f(x)=\left\{\begin{matrix}0.08x & x \leq 7500\\ 600+0.16(x-7500) & 7500 < x \leq 15000\\ 1800+0.20(x-15000) & 15000 < x\end{matrix}\right.`

Since, 9500 lies between 7500 and 15000,

Therefore, the commission would be,

f(9500)= 600 + 0.16(9500 - 7500) = 600 + 320 = $ 920