Jessica has 48 coins, some of them are nickels and some are dimes. How many of each does she have if she has $3.25 total?

Jessica will have 17 Dimes and 31 Nickels.

Nickel = 0.05

Dime = 0.10

XNickels + YDimes = 3.25

0.05X + 0.1Y = 3.25

You could do this using trial and error.

You know the maximum amount of dimes you could have is 32. Because 32 * 0.1 = 3.20. If you had 33 dimes, you'd go over the limit.

You also know you need to have 48 coins. If you have 32 dimes and 1 nickel, you will not have 48 coins.

You can try any number below 32. I will try 16 because it's half of 32.

16 * 0.1 = 1.60

48 - 16 = 32 coins left

32 * 0.05 = 1.60

1.60 + 1.60 = 3.20

We're a nickel off, therefore we need to remove a nickel and add a dime.

17 * 0.1 = 1.70

48 - 17 = 31

31 * 0.05 = 1.55

1.70 + 1.55 = 3.25

Jessica will have 17 Dimes and 31 Nickels.