SOLUTION: Jennifer went on a shopping spree, spending a total of 124.00 on a skirt, a sweater and a pair of shoes. The cost of the sweater was 8/7 of the cost of the skirt. The shoes cost 8.

Question 437098: Jennifer went on a shopping spree, spending a total of 124.00 on a skirt, a sweater and a pair of shoes. The cost of the sweater was 8/7 of the cost of the skirt. The shoes cost 8.00 less then the skirt. Find the cost of each item
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x = price of skirt
y = price of sweater
z = price of shoes
.
We're told...
x + y + z = 124
y = 8/7*x
z = x -8 or x = z+8
.
Now we have y and z defined in terms of x.
So, we can put them all together with what we know.
.
x + 8/7*x + (x-8) = 124
Multiply both sides by 7 to eliminate the denominator
7x + 8x + 7(x-8) = 7*124
15x + 7x -56 = 868
22x = 868 + 56
22x = 924
x = 42
.
The skirt cost $42.
The shoes cost $8 less than the skirt, 42-8 = 34.
The shoes cost $34.
The total is $124, so the sweater cost 124 - 42 - 34 = 48.
The sweater cost $48.
.
Always check your answer!
There's no need to check the total, since we plugged it into the equations to ensure it was 124.
Likewise, there's no need to check the shoes, since we did the same.
So, we're left with calculating the price of the sweater to see if it matches.
.
8/7*x = 8/7*42
8/7*42 = 8*6
8*6 = 48
That checks.
.
Always make sure your answer is stated clearly.
The skirt cost $42.
The shoes cost $34.
The sweater cost $48.
.
Done.
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