SOLUTION: Jennifer went on a shopping spree, spending a total of $166 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 $12

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Jennifer went on a shopping spree, spending a total of $166 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 $12      Log On


   

Question 1015156: Jennifer went on a shopping spree, spending a total of $166 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 $12 more than the skirt. Find the cost of each item.
Please help me solve this.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost of the skirt
Let +b+ = the cost of the sweater
Let +c+ = the cost of the pair of shoes
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(1) +a+%2B+b+%2B+c+=+166+
(2) +b+=+%288%2F7%29%2Aa+
(3) +c+=+a+%2B+12+
----------------------
Substitute (2) and (3) into (1)
(1) +a+%2B+%288%2F7%29%2Aa+%2B+a+%2B+12+=+166+
(1) +%2814%2F7%29a+%2B+%288%2F7%29%2Aa+=+166+-+12+
(1) +%2822%2F7%29%2Aa+=+154+
Multiply both sides by +7%2F22+
(1) +a+=+%287%2F22%29%2A154+
(1) +a+=+7%2A7+
(1) +a+=+49+
------------------
(2) +b+=+%288%2F7%29%2Aa+
(2) +b+=+%288%2F7%29%2A49+
(2) +b+=+8%2A7+
(2) +b+=+56+
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(3) +c+=+a+%2B+12+
(3) +c+=49+%2B+12+
(3) +c+=+61+
------------------
The cost of the skirt was $49
The cost of the sweater was $56
The cost of the pair of shoes $61
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Check:
(1) +a+%2B+b+%2B+c+=+166+
(1) +49%2B+56+%2B+61+=+166+
(1) +166+=+166+
OK