Question

A collection of nickels, dimes, and quarters consist of
11
coins with a total of
$1.35
. If the number of dimes is equal to the number of nickels, find the number of each type of coins.

Answer 1

Quarters (q) = 25 cent, nickles (n) = 10 cent, dime (d)  = 5 cent:

q + n + d  = 11 coins
25*q + 10*n + 5*d = 135 cents
d = n

Then:

q + 2n = 11 and 25q + 15n = 135

q+2n=11 and 5q + 3n = 27

q = 11-2n -----> 5*(11-2n)+3n = 27

55 -10n+3n=27, or -7n = -28, n = 4 (nice!)

So, 4 nickle, 4 dime and 3 (11-2*4) quarters.

Check it works! ($1.35!)