Call the nickels = n
Call the dimes = d
Equations.
n + d = 15 (1)
0.05n + 0.10d = 0.90 Multiply through by 100
5n + 10d = 90 Divide by 5
n + 2d = 18 (2)
Solve
Begin by subtracting (1) from (2)
n + 2d = 18
n + d = 15 the ns cancel out.
d = 3
Now put this result into equation (1)
n + d = 15
n + 3 = 15 Subtract 3 from both sides.
n = 15 - 3
n = 12
Check
5n + 10d = 90
5*12 + 3*10 = ?90
60 + 30 = 90 and it does check
Note the trick with this problem is to get rid of the decimals.
It makes it much easier to work with whole numbers.