How many ways can you make 50 cents using only nickels and dimes?

Answer 1

Assuming I can use nickels and/or dimes my formula looks like this:

10x + 5y = 50

We can put this into slope intercept form as follows:

y = -2x +10 where both x and y must be ≥ 0 (can't have negative coins)

The line segment so described starts at point (0,10) [zero dimes, 10 nickels] and runs through 4 other points, ending at (5,0) [5 dimes, zero nickels].

Alternatively, I could make a chart by using different values for x and solving for y:

x y

0 10

1 8

2 6

3 4

4 2

5 0

Either way, the answer is 6 permutations or ways to make 50 cents with dimes and/or nickels.

Note: If the problem required that both nickels and dimes always be used, then there are only 4 soultions.