# Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many nickels do you have? ##### 1 Answer Mar 4, 2018 See a solution process below: #### Explanation: First, let's call the number of quarters you have: $q$And, the number of nickels you have: $n$Using these variables and the information in the problem we can write two equations: • Equation 1: $q + n = 25$• Equation 2: $0.25q + $0.05n =$3.45

Step 1) Solve the first equation for $q$:

$q + n = 25$

$q + n - \textcolor{red}{n} = 25 - \textcolor{red}{n}$

$q + 0 = 25 - n$

$q = 25 - n$

Step 2) Substitute $\left(25 - n\right)$ for $q$ in the second equation and solve for $n$ to find the number of nickels you have:

$0.25q +$0.05n = $3.45 becomes: $0.25(25 - n) + $0.05n =$3.45

($0.25 xx 25) - ($0.25 xx n) + 0.05n = $3.45 $6.25 - $0.25n + 0.05n =$3.45

$6.25 + (-$0.25 + 0.05)n = $3.45 $6.25 + (-$0.20)n =$3.45

$6.25 -$0.20n = $3.45 $6.25 - color(red)($6.25) -$0.20n = $3.45 - color(red)($6.25)

0 - $0.20n = -$2.80

-$0.20n = -$2.80

(-$0.20n)/(color(red)(-)color(red)($)color(red)(0.20)) = (-$2.80)/(color(red)(-)color(red)($)color(red)(0.20))

(color(red)(cancel(color(black)(-$0.20)))n)/cancel(color(red)(-)color(red)($)color(red)(0.20)) = (color(red)(cancel(color(black)(-$)))2.80)/(cancel(color(red)(-)color(red)($))color(red)(0.20))

$n = \frac{2.80}{\textcolor{red}{0.20}}$

$n = 14$

You would have 14 nickels