SOLUTION: Eleanor claims: "It is possible for 46 pennies and nickels to have a total value of a dollar." Is she right or wrong? Give a convincing argument to justify your answer.

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Question 218115: Eleanor claims: "It is possible for 46 pennies and nickels to have a total value of a dollar." Is she right or wrong? Give a convincing argument to justify your answer.
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = # pennies,,,,,y=# nickels
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.01x +.05y =1.00,,,,,but x+y=46,,,,or y=46-x,,,,,,subst
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.01x +.05(46-x) = 1.00
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.01x +2.30 -.05x =1.00
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-.04x = -1.30
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x=32.5,,,,,,,,,,y=13.5
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check,,,.01(32.5) +.05(13.5) = .325 +.675 =1.00,,,,,ok
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since the money required to reach $1.00 is not in even numbers for the pennies or nickels,,,,it is NOT possible to make $1 even.
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