Multiply both sides of the second equation by 100 to get rid of the decimals:
0.05n + 0.10d = 1.50
==> 5n + 10d = 150
Multiply both sides of the first equation by -5:
n + d = 21
==> -5n - 5d = -105
Add the two equations together:
(5n + 10d) + (-5n - 5d) = 150 + (-105)
Notice that the terms containing n get eliminated and we can solve for d :
(5n - 5n) + (10d - 5d) = 150 - 105
5d = 45
d = 45/5 = 9
Plug this into either original equation to solve for n. Doing this with the first equation is easiest:
n + 9 = 21
n = 21 - 9 = 12
So Donna used 12 nickels and 9 dimes.
