Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The tot

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type?

Let d be dimes and q be quarters. Set up two equations from our givens:

1. d + q = 41
2. 0.1d + 0.25q = 7.85

Rearrange (1) by subtracting q from each side:
(3) d = 41 - q

Now, substitute (3) into (2)
0.1(41 - q) + 0.25q = 7.85
4.1 - 0.1q + 0.25q = 7.85

Combine q terms
0.15q + 4.1 = 7.85

Using our equation calculator, we get:
q = 25

Substitute q = 25 into (3)
d = 41 - 25
d = 16