# Each are of quarters and nickels is worth $3.70. There are 22 coins in all How many of there? ##### 1 Answer Jan 9, 2017 First, let's call the number of nickels we have $n$and the number of quarters $q$. Now we can write two equations which we can use to solve the problem through substitution: First we know there are 22 coins in total, therefore: $n + q = 22$And we know their value is$3.70 so we can write:

$0.05 n + 0.25 q = 3.70$

Step 1) solve the first equation for $n$

$n + q = 22$

$n + q - \textcolor{red}{q} = 22 - \textcolor{red}{q}$

$n + 0 = 22 - \textcolor{red}{q}$

$n = 22 - q$

Step 2) Substitute $22 - q$ for $n$ in the second equation and solve for $q$.

$0.05 \left(22 - q\right) + 0.25 q = 3.70$

$\left(0.05 \times 22\right) - \left(0.05 \times q\right) + 0.25 q = 3.70$

$1.1 - 0.05 q + 0.25 q = 3.70$

$1.1 + 0.25 q - 0.05 q = 3.70$

$1.1 + \left(0.25 - 0.05\right) q = 3.70$

$1.1 + 0.20 q = 3.70$

$1.1 - \textcolor{red}{1.1} + 0.20 q = 3.70 - \textcolor{red}{1.1}$

$0 + 0.20 q = 2.60$

$0.20 q = 2.60$

$\frac{0.20 q}{\textcolor{red}{0.20}} = \frac{2.60}{\textcolor{red}{0.20}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{0.20}}} q}{\cancel{\textcolor{red}{0.20}}} = 13$

$q = 13$

Step 3) Substitute $13$ for $q$ in the solution to the first equation in Step 1.

$n = 22 - 13$

$n = 9$

Solution:

There are 9 nickels and 13 quarters