Question

Norman makes $15 commission for selling $200 in merchandise. He makes $37.50 commission for selling $500 in merchandise. Assuming that the variables are directly related and Norman wants to make $150 in commission, what is the total value of merchandise he needs to sell? $335.00 $612.50 $2,000.00 $5,000.00

Answer 1

15 is what percent of 200...
15/200 = x/100
cross multiply
200x = 1500
x = 1500/200
x = 7.5%

so Norman makes 7.5% commission on all his sales

so if he wants to make 150......7.5% of what is 150...
0.075x = 150
x = 150 / 0.075
x = 2000 <== he would have to sell $ 2000 worth of merchandise

Answer 2

Norman needs to sell merchandise of $2,000 for a commission of $150.

Given to us,

For first merchandise,

merchandise price = $200

Commission on merchandise = $15

For Second merchandise,

merchandise price = $500

Commission on merchandise = $37.50

Percentage Commission For first merchandise,

$\rm{Percentage\ Commission =\dfrac{Commission\ on\ merchandise}{merchandise\ price} = \dfrac{\ 15}{\ 200} = 0.075 = 7.5 \%$

Percentage Commission For Second merchandise,

$\rm{Percentage\ Commission =\dfrac{Commission\ on\ merchandise}{merchandise\ price} = \dfrac{\ 37.50}{\ 500} = 0.075 = 7.5 \%$

As we can see that the percentage commission on both the merchandise is the same. therefore, the percentage commission for every piece of merchandise will be the same.

For $150 in commission

$\rm{Percentage\ Commission =\dfrac{Commission\ on\ merchandise}{merchandise\ price}$

$\dfrac{7.5}{100}= \dfrac{\ 150}{x}$

$x= \dfrac{\ 150\times 100}{7.5}\\x = \ 2000$

Hence, Norman needs to sell merchandise of $2,000 for a commission of $150.