SOLUTION: A particular style of sunglasses costs the retailer $80 per pair. At what price should the retailer mark them so he can sell them at a 20% discount off the selling price and still

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Question 1016960: A particular style of sunglasses costs the retailer $80 per pair. At what price should the retailer mark them so he can sell them at a 20% discount off the selling price and still make 30% profit on his cost?
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A particular style of sunglasses costs the retailer $80 per pair. At what price should the retailer mark them so he can sell them at a 20% discount off the selling price and still make 30% profit on his cost?
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Let that price be "x":::
0.8x = 1.3(80)
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0.8x = 104
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x = $130
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Cheers,
Stan H.
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Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the equations used would be:

p = s - c

this means profit = sale price minus cost

s = .8 * m

this means sale price is 80% of the markup price.
sale price is 80% of the markup price because if you subtract 20% of the markup price from the markup price, you are left with 805 of the markup price.

p = s - c becomes:

p = .8 * m - c

you know that p = .3 * c

that means that the profit is equal to 30% of the cost.

p = .8 * m - c becomes .3 * c = .8 * m - c

add c to both sides of this equation to get .3 * c + c = .8 * m

combine like terms to get 1.3 * c = .8 * m

divide both sides of this equation by .8 to get (1.3/.8) * c = m.

solve for m to get m = (1.3/.8) * c = 1.625 * c.

you know that c = 80, therefore m = 1.625 * 80 = 130.

the markup price needs to be 130 dollars.
the sale price is 20% off of the markup price.
this makes the sale price equal to 130 - 26 = 104 dollars.
the cost is 80 dollars.
the profit is 104 - 80 = 24 dollars.
24/80 = .3 = 30% of 80.
the profit is 30% of the cost.