Question

a collection of dimes and nickels is worth $8.40 there are 106 coins how many of each are there

Answer 1

There are 62 dimes and 44 nickels.

N + D = 106 (There are 106 coins in all.)
1 nickel = 5 cents.
1 dime = 10 cents.
5*N + 10*D = 840 ($8.40 = 840 cents)
N + D = 106 -------(1)
N = (106 - D)
5*N + 10*D = 840 ---------(2)
5*(106-D) + 10*D = 840
530 - 5*D + 10*D = 840
5*D = 840 - 530
5*D = 310
D = 310/5 = 62
Eq(1) N + D = 106
N + 62 = 106
N = 106 - 62
N = 44