# 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? ##### 1 Answer Nov 26, 2016 Zoe has 5 nickles and 11 dimes. #### Explanation: First, let's give what we are trying to solve for names. Let's call the number of nickles $n$and the number of dimes $d$. From the problem we know: $n + d = 16$She has 16 coins made up of some dimes and some nickles. $0.05 n + 0.1 d = 1.35$The value of the dimes with the value of the nickles is$1.35.

Next, we solve the first equation for $d$

$n + d - n = 16 - n$

$d = 16 - n$

Next, we substitute $16 - n$ for $d$ in the second equation and solve for $n$:

$0.05 n + 0.1 \left(16 - n\right) = 1.35$

$0.05 n + 0.1 \cdot 16 - 0.1 n = 1.35$

$\left(0.05 - 0.1\right) n + 1.6 = 1.35$

$- 0.05 n + 1.6 = 1.36$

$- 0.05 n + 1.6 - 1.6 = 1.35 - 1.6$

$- 0.05 n = - 0.25$

$\frac{- 0.05 n}{- 0.05} = \frac{- 0.25}{- 0.05}$

$n = 5$

Now we can substitute $5$ for $n$ in the solution for the first equation and calculate $d$:

$d = 16 - 5$

$d = 11$