Mike F.

asked • 01/15/18

Terry has 85 cents in nickels and quarters. Find all the possibilities for the number of each type of coin that terry can have

I need help solving his word problem

Arturo O.

n = number of nickels at 5 cents each
q = number of quarters at 25 cents eack

85 = 5n + 25q,

subject to the condition that both n and q are integers ≥ 0.

17 = n + 5q
 
Now look for combinations of n = 0,1,2,.. with combinations of q = 0,1,2,... that satisfy the equation.  This is an example of a Diophantine problem, i.e. a problem whose solutions must be integers.
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01/15/18

1 Expert Answer

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Mark M. answered • 01/15/18

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25, 25, 25, 5, 5                
 
25, 25, 5, 5, 5, 5, 5, 5, 5 
25, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 
 
He could have three quarters and two nickels.
He could have two quarters and 7 nickels
He could have one quarter and 12 nickels
Since his money is in quarters and nickels, the all nickels option is out.
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