SOLUTION: Claire bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item. MUST Show Work!

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Claire bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item. MUST Show Work!      Log On

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Question 68795: Claire bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item.
MUST Show Work!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Claire bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item.
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1st: 3b+5s=2.31
2nd: 5b+3s=3.05
Multiply 1st by 5 to get:
3rd: 15b+25s=11.55
Multiply 2nd by 3 to get:
4th: 15b+9s=9.15
Subtract 4th from 3rd to get:
16s=2.4
s=0.15 or 15 cents (cost of bar of soap)
Substitute into 1st to solve for b:
3b+5(0.15)=2.31
3b+0.75=2.31
3b=1.56
b=0.52 or 52 cents (cost of a sponge)
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Cheers,
Stan H.