SOLUTION: How many ways can Ally make 45 cents using nickels, dimes, and quarters?

Question 291027: How many ways can Ally make 45 cents using nickels, dimes, and quarters?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=the number of nickels that he can use
Let y=number of dimes that he can use
And he can only use 0 or 1 quarter
If he doesn't use any quarters then we have:
5x+10y=45 or
x+2y=9
solve for x
x=9-2y Now we know two very important things; x & y must be whole, positive integers.
that means that y<=4 (Do you know why?)
if y=0, x=9---------------------solution--9 nickels, 0 dimes 0 quarters
if y=1, x=7--------------------solution----7 nickels, 1 dime, 0 quarters
if y=2, x=5------------solution----5 nickels, 2 dimes, 0 quarters
if y=3, x=3---------------solution---3 nickels, 3 dimes, 0 quarters
if y=4, x=1------------------solution---1 nickel, 4 dimes, 0 quarters
That is all for the case where we don't use any quarters
If he uses 1 quarter then we have:
5x+10y+25=45 or
x+2y=4
same as before
x=4-2y
y<=2
if y=0, x=4---------------solution-----4 nickels, 0 dimes, 1 quarter
if y=1, x=2----solution---2 nickels, 1 dime, 1 quarter
if y=2, x=0-----solution---0 dickels, 2 dimes, 1 quarter
Hope this helps ---ptaylor
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