Question 1091966: A buyer wants to offer a pre- Easter special of leather handbags that will sell for $45 each. In the market, he purchases for this event 75 pieces that cost $22.50 each. From the same resource, he buys for regular stock 50 straw handbags that cost $15 each. At what price should he retail the straw handbags to achieve a 48% markup on the entire purchase?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he buys 75 leather handbags at 22.50 each for a total cost of 1687.5.
he buys 50 straw handbags at 15.00 each for a total cost of 750.
his total cost if 1687.50 + 750.00 = 2437.5
in order to have a 48% markup, the selling price must be 48% greater than the cost.
the cost is 2437.5
48% of 2437.5 is equal to .48 * 2437.5 which is equal to 1170.
the selling price must be 1170 dollars greater than the cost.
the total selling price is 75 * 45 + 50 * x
x represents the selling price of the straw handbags.
therefore, the selling price of 75 * 45 + 50 * x minus the cost of 2437.5 must be equal to 1170 dollars.
the equation is therefore 75 * 45 + 50 * x - 2437.5 = 1170
add 2437.5 to both sides of this equation to get 75 * 45 + 50 * x = 3607.5
simplify to get 3375 + 50 * x = 3607.5
subtract 3375 from both sides of this equation to get 50 * x = 232.5
divide both sides of this equation by 50 to get x = 4.65.
in order to get an overall markup of 48%, he needs to sell the straw handbags for 4.65 each.
since each handbag cost 15 dollars, then he is selling each at a loss of 10.35.
this is necessary because the markup on the leather handbags is 100% since they cost 22.50 each and are being sold for 45.00 each.
in order to get the overall markup to be 48%, he had to sell the straw handbags at a loss.
if he sold them at cost, the overall markup would be greater than 48%.
consider overall sale price of 75 * 45 + 50 * 15 = overall sale price of 4125.
4125/2437.5 = 1.69 0 1 = 69 = 69% overall markup.
selling the straw hats at cost would have given him an overall markup of 69% which is more than the 48% he wanted.
bottom line:
straw hats are sold at a loss in order to make the total markup equal 48%.
looks a little strange but that's the way it comes out.
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