SOLUTION: Jack has dimes, nickels, and quarters worth $10.00. If he has 50 coins in total, how many coins will Jack have of each?

Question 848318: Jack has dimes, nickels, and quarters worth $10.00. If he has 50 coins in total, how many coins will Jack have of each?
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
d count of dimes
n count of nickels
q count of quarters

and .
Simplify the money count equation for whole number coefficients.

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SYSTEM:
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2d+n+5q=200
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d+n+q=50
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That is two equations and three unknown variables. Something must be initially assumed constant. Try taking n as a constant, k=n.

SYSTEM with k=n:
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2d+5q=200-k
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d+q=50-k
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Try elimination. Multiply the second equation by 2 and subtract from the first equation.

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Try elimination again for the other variable. Multiply the second equation by 5 and ...

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A choice must be found of some whole number for k so that d and q each are also whole numbers. MAYBE k=2 worth a test.
k_____________q____________d
2____________34____________14----------Combination appears to work, since k+q+d=50.

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ANSWER: A good result then is 2 nickels, 14 dimes, 34 quarters.
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