Question 535195: Jose has been collecting quarters and nickels. He empites his wallet to find that he has 32 coins (only quarters and nickels) worth $4.40. How many quarters and how many nickels does Jose have
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! Let Q = # quarters
Let N = # nickels
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Given two facts:
Q + N = 32
.25Q + .05N = 4.40
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The basic method is to isolate one of the unknowns in one of the equations and then substitute that equality back into the other equation.
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Restate 1st equation as Q = 32 - N
Substitute this into the 2nd equation:
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.25(32 - N) + .05N = 4.40
8 - .25N + .05N = 4.40
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Simplify by combining all like terms and rearrange:
8 - .20N = 4.40
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Add .20N to both sides:
8 - .20N + .20N = 4.40 + .20N
8 = 4.40 + .20N
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Subtract 4.40 from both sides:
8 - 4.40 = 4.40 - 4.40 + .20N
3.60 = .20N
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Multiply both sides by 5 (so we get a whole N)
5(3.60) = 5(.20N)
18 = N
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This represents the # of nickels as we set up the problem. Let's go back and find Q, the # of quarters then check our work:
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From 1st equation, Q + N = 32, restated as Q = 32 - N, solve for Q:
Q = 32 - (18)
Q = 14
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Check N = 18 and Q = 14 against the 2nd equation:
.25(14) + .05(18) = 4.40
3.50 + .90 = 4.40
4.40 = 4.40 checks
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Q = 14 and N = 18 are the answers to the problem.
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cheers,
Lee
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