# A person has a total of 65 coins in a jar consisting of quarters and nickles. The total value of the coins is $10.25. How many quarters and nickles does the person have? ##### 1 Answer Jun 14, 2017 See a solution process below: #### Explanation: First: Let's call the number of quarters: $q$Let's call the number of nickles: $n$We know: $q + n = 65$because there are 65 coins in the jar. We also know multiplying the value of the coins by the number of coins gives: 0.25q + 0.05n =$10.25

Step 1) We can now solve the first equation for $q$:

$q + n = 65$

$q + n - \textcolor{red}{n} = 65 - \textcolor{red}{n}$

$q + 0 = 65 - n$

$q = 65 - n$

Step 2) Substitute $\left(65 - n\right)$ for $q$ in the second equation and solve for $n$:

$0.25 q + 0.05 n = 10.25$ becomes:

$0.25 \left(65 - n\right) + 0.05 n = 10.25$

$\left(0.25 \cdot 65\right) - \left(0.25 \cdot n\right) + 0.05 n = 10.25$

$16.25 - 0.25 n + 0.05 n = 10.25$

$16.25 + \left(- 0.25 + 0.05\right) n = 10.25$

$16.25 + \left(- 0.2\right) n = 10.25$

$16.25 - 0.2 n = 10.25$

$- \textcolor{red}{16.25} + 16.25 - 0.2 n = - \textcolor{red}{16.25} + 10.25$

$0 - 0.2 n = - 6$

$- 0.2 n = - 6$

$\frac{- 0.2 n}{\textcolor{red}{- 0.2}} = - \frac{6}{\textcolor{red}{- 0.2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 0.2}}} n}{\cancel{\textcolor{red}{- 0.2}}} = 30$

$n = 30$

Step 3) Substitute $30$ for $n$ in the solution to the first equation at the end of Step 1 and calculate $q$:

$q = 65 - n$ becomes:

$q = 65 - 30$

$q = 35$

The solution is: $n = 30$ and $q = 35$

So there are $30$ nickles and $35$ quarters.