number of dimes ---- x
number of quarters --- 21-x
10x + 25(21-x) = 405
10x + 525 - 25x = 405
-15x = -120
x = 8
so 8 dimes and 21-8 or 13 quarters
dimes ---- d
based on numbers:
d+q = 21
based on value:
10d + 25q = 405 --- 2d + 5q = 81
double the first:
2d + 2q = 42
subtract from the 2nd to give
3q = 39
q = 13
back into the first:
d + q = 13
d = 8
I find the first method easier.
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