Zoe has a total of 16 coins. Some of her coins are dimes and some are nickels. The combined value of her nickels and dimes is $1.35. How many nickels and dimes does she have?

11 dimes, 5 nickels

Step-by-step explanation:

You have two different equations here.

d+n=16 (number of dimes plus number of nickels equals 16 total coins) and

.1d+.05n=1.35 (number of dimes times. 1 (the value of a dime is 10 cents) plus number of nickels times. 05 (the value of a nickel is 5 cents) equals 1.35 (the total value of the coins)

The first equation can become either d=16-n or n=16-d. I went with the second one, but it doesn't matter.

The second equation can be multiplied (both sides) by 100 just to make the math easier. It then becomes 10d+5n=135. Now, take the first equation and put it into the second one. Substitute the variable for the first equation. Since I did d=16-n, my new equation was 10 (16-n) + 5n=135.

This simplifies to 160-10n+5n=135

Combine like terms and you get - 5n=-25

Divide n=5. Zoe has 5 nickels. Now, put that information into the first equation.

d=16-n. n=5

d=16-5

d=11. Zoe has 11 dimes