math
posted by m on .
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

number of dimes  x
number of quarters  21x
by value:
10x + 25(21x) = 405
10x + 525  25x = 405
15x = 120
x = 8
so 8 dimes and 218 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.