SOLUTION: Mrs. Johnson planned to spend $78 for fabric to make draperies.She found her fabric on sale at 20 percent less per yard than she expected and was able to buy her drapery fabric plu

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Question 159990: Mrs. Johnson planned to spend $78 for fabric to make draperies.She found her fabric on sale at 20 percent less per yard than she expected and was able to buy her drapery fabric plus 4 extra yards for a bedspread for $83.20. How much fabric had she planned to buy and what was the original cost per yard?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Mrs. Johnson planned to spend $78 for fabric to make draperies. She found her
fabric on sale at 20 percent less per yard than she expected and was able to
buy her drapery fabric plus 4 extra yards for a bedspread for $83.20.
How much fabric had she planned to buy and what was the original cost per yard?
:
Let x = amt of fabric she planned to buy
then
(x+4) = amt she ended up buying
:
Presale price per yard = 78%2Fx
:
20% off price per yard = .8*78%2Fx = 62.4%2Fx
:
Actual price per yard = 83.20%2F%28%28x%2B4%29%29
:
20% off = Actual price
62.4%2Fx = 83.20%2F%28%28x%2B4%29%29
cross multiply
83.2x = 62.4(x+4)
:
83.2x = 62.4x + 249.6
:
83.2x - 62.4x = 249.6
:
20.8x = 249.6
x = 249.6%2F20.8
x = 12 yds she planned to buy
:
Presale price = 78%2F12 = $6.50 per yd
:
:
Check solution by finding the actual price per yard:
83.20%2F%28%2812%2B4%29%29 = 83.20%2F16 = $5.20 per yd
Is it equal to 20% off of $6.50 a yard?
.8 * 6.5 = $5.20, hurray, it is!