How Much ?

Question

A consignment shop accepts an item of clothing that no longer fits (or one you have grown tired of) and sells it for you. The shop then charges you an agreed on percent of the selling price as their profit. Suppose the owner of a designer wool coat would like to make $210 on its sale at a consignment shop. If there is a 12 1/2% consignment charge, for what price must the coat be sold?

Answer 1

Okay this question is interpreted in the following manner. To sell the item, the price minus the price times the consignment fee equals the amount the owner wish to sell the item for.

In your example this follows as:

x - 0.125x = $210

x = the actual sale price and 0.125 is the decimal equivalent of 12.5%

Therefore since x has a coefficient of 1 you would have 1 - 0.125 = 0.875

so the equation becomes 0.875x = $210 and  x = $210/0.875 = $240

Finally the consignment fee = $240 - $210 = $30 which is also calculated as part of the original equation:

0.125x = The consignment fee

0.125($240) = The consignment fee

$30 = The consignment fee

Hope this helps!

Art

Answer 2

so if the shop keeps 12.5% of what the coat brings in and you want to make $210, that means that 210 has to be 87.5% of the total asking price. (100%-12.5%=87.5%)

This means that 210= .875* T (T=total price)

 re-arrange the equation so 210/.875= T    T=240    The consignment fee is $30

Total price is $240       Ans.=$240

Hope this helps

  -Jeff