Question

Pear's music store pays its sales staff a commission of 9.5% of the first $1,000 in sales and 15.5% of the balance in sales. Alex, the store’s drum expert, received $1,234.25 in commission last week. What were his total sales for the week?

Answer 1

Total sales for the week is $8350 for the commission received $1234.25 last week

Given:

9.5% commission for first 1000

15.5 % for the remaining sales amount.

Total received 1234.25

To find :

Total sales amount  for the week

Explanation :

Let x be the total sales amount .

9.5 % for first 1000. So its $\frac{9.5}{100} \cdot 1000=95$

15.5 % for the remaining sales amount. so we have to find commission for remaining amount x-1000

$0.155 \cdot (x-1000)$

Total commission = $95+0.155 \cdot (x-1000)$

we know that commission is 1234.25. Replace it and solve for x

$95+0.155\left(x-1000\right)=1234.25\\95\cdot \:1000+0.155\left(x-1000\right)\cdot \:1000=1234.25\cdot \:1000\\95000+155\left(x-1000\right)=1234250\\\mathrm{Subtract\:}95000\mathrm{\:from\:both\:sides}\\155\left(x-1000\right)=1139250\\\mathrm{Divide\:both\:sides\:by\:}155\\\frac{155\left(x-1000\right)}{155}=\frac{1139250}{155}\\\\x-1000=7350\\Add 1000\\x=8350$

Total sales for the week is $8350

Learn more:  brainly.com/question/11443414