Question

"Sarah has 43 coins in her purse made up of only nickels and quarters. She runs her change through the bank coin machine and gets back $7.75. How many nickels and quarters did she start with?"

Answer 1

15 nickels and 28 quarters.

Step-by-step explanation:

Let the number of nickels = n

Let the number of quarters = q

Sarah has 43 coins:

`\begin{gathered} n+q=43 \\ \implies n=43-q \end{gathered}`

1 nickel = 5 cents = $0.05

1 quarter = 25 cents =$0.25

She runs her change through the bank coin machine and gets back $7.75

`0.05n+0.25q=7.75`

We then solve the two equations simultaneously:

`\begin{gathered} 0.05n+0.25q=7.75 \\ 0.05(43-q)+0.25q=7.75 \\ 2.15-0.05q+0.25q=7.75 \\ 0.2q=7.75-2.15 \\ 0.2q=5.6 \\ q=28 \end{gathered}`

Finally, solve for the number of nickels:

`\begin{gathered} n=43-q \\ =43-28 \\ n=15 \end{gathered}`

Sarah started with 15 nickels and 28 quarters.