Question

Sasha earns a $36,500 per year in salary and 12% commission on her sales at her job selling hair products to salons. What would her total sales have to be in order for her total income to fall between $52,000 and $58,000?

Answer 1

`color(blue)($129166.67 < "Sales value" < $179166.67)`

Explanation:

Given: Salary only is $36500

So the commission range added to her salary is

`$52000" "$58000`
`ul($36500)" "ul($36500) larr" subtracting salary"`
`$15500" to "$21500 larr" range of commission (between)"`

`color(brown)("The use of the word 'between' means that it can not actually be those values.")`

Let the top of the sales range be `t`
Let the bottom of the sales range be `b`

Then

`12/100t=$21500" " =>" " color(brown)(t=$179166.67" to 2 decimal places")`

`12/100b=$15500" "=>" "color(brown)(b=$129166.67" to 2 decimal places")`

`color(blue)($129166.67 < "Sales value" < $179166.67)`