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Question

# Use a system of equations to solve the following problems. See the earlier examples.Karen empties out her purse and finds 45 loose coins, consisting entirely of nickels and pennies. If the total value of the coins is $\ 1.37$, how many nickels and how many pennies does she have?

Solution

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The given situation can be used to form 2 equations. Therefore, let $n$ be the number of nickel coins and $p$ be the number of pennies. Together the sum of coin is equal to 45. Form Equation 1:

$\begin{equation*} n+p=45 \end{equation*}$

Now use the values of nickel and penny and the their total worth to form Equation 2:

$\begin{equation*} 0.05n+0.01p=1.37 \end{equation*}$

Note that the unit here is dollars so the value of nickel and pennies has been converted.

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