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?

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Answer 1 · 2016-11-06T14:22:45

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

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)#