Question

A man has 21 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 405 cents, how many dimes and how many quarters does he hav

Answer 1

number of dimes ---- x
number of quarters --- 21-x

by value:
10x + 25(21-x) = 405
10x + 525 - 25x = 405
-15x = -120
x = 8

so 8 dimes and 21-8 or 13 quarters

or

dimes ---- d
quarters ---q

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.