Question

At 7-11, I get my change from a Slurpee in all nickels and pennies. If I get $0.87 in change, and a total of 31 coins, how many of each coin did I get in change? For full credit, use an algebraic method here!

Answer 1

Given:

The change all in nickels and pennies.

Let the number of nickels = x

Let the number of pennies = y

Total coins = 31

so, x + y = 31

1 nickel = 5 cents

1 penny = 1 cent

The change = $0.87 = 87 cents

so, 5x + y = 87

so, we have the following system of equations:

$\begin{gathered} x+y=31\rightarrow(1)\times-1 \\ 5x+y=87\rightarrow(2) \\ ------------- \\ (5x-x)+(y-y)=87-31 \\ \\ 4x=56 \\ \\ x=\frac{56}{4}=14 \\ \\ y=31-14=17 \end{gathered}$

So, the number of nickels = x = 14

And the number of pennies = y = 17