SOLUTION: The marked price of a pillow is $240. The shop makes a profit of 28% by selling the pillow at a discount of 20%.If the pillow is sold at the marked price, find the profit percent

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Question 1174193: The marked price of a pillow is $240. The shop makes a profit of 28% by selling the pillow at a discount of 20%.If the pillow is sold at the marked price, find the profit percent
Answer by Theo(13342) (Show Source):
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the marked price is 240.
the pillow is sold at a discount of 20% off the marked price.
240 - .2 * 240 = 192.
that's the price the pillow was sold at.
the shop made a profit of 28% over the cost of the pillow.
let x = the cost of the pillow.
your equation to solve is:
x + .28 * x = 192
combine like terms to get:
1.28 * x = 192
divide both sides of this equation by 1.28 to get:
x = 192 / 1.28 = 150.

the cost of the pillow was 150.
if the pillow was sold at the marked price of 240, then the profit would have been 240 - 150 = 90.
the profit margin would have been 90 / 150 = .6 * 100 = 60%.

confirm as follows:

cost is 150.
1.28 * 150 = 192
1.60 * 150 = 240
.8 * 240 = 192

1.28 * 150 is the same as 150 + .28 * 150
1.60 * 150 is the same as 150 + .60 * 150
.8 * 240 is the same as 240 - .2 * 240

this is done by factoring out the common term in the expression.

start with 150 + .28 * 150 and factor out the common term of 150 to get (1 + .28) * 150 and simplify the terms in the parentheses to get 1.28 * 150.

start with 150 + .60 * 150 and factor out the common term of 150 to get (1 + .60) * 150 and simplify the terms in the parentheses to get 1.60 * 150.

start with 240 - .2 * 240 and factor out the common term of 240 to get (1 - .2) * 240 and simplify the terms in the parentheses to get .8 * 240.