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?
:
Let x = amt of fabric she planned to buy
then
(x+4) = amt she ended up buying
:
Presale price per yard = {{{78/x}}}
:
20% off price per yard = .8*{{{78/x}}} = {{{62.4/x}}}
:
Actual price per yard = {{{83.20/((x+4))}}}
:
20% off = Actual price
{{{62.4/x}}} = {{{83.20/((x+4))}}}
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 = {{{249.6/20.8}}}
x = 12 yds she planned to buy
:
Presale price = {{{78/12}}} = $6.50 per yd
:
:
Check solution by finding the actual price per yard:
{{{83.20/((12+4))}}} = {{{83.20/16}}} = $5.20 per yd
Is it equal to 20% off of $6.50 a yard?
.8 * 6.5 = $5.20, hurray, it is!