Question

After all your Christmas shopping is done, you are running low on money. When you count the money in your pocket, you find out only nickels and dimes are in there. If 31 coins in your pocket have a value of $2.65, how many nickels and how many dimes are in your pocket?

Answer 1

Let n be the number of nickels

Let d be the number of dimes

There are 31 coins in your pocket:

`n+d=31`

You have in total $2.65:

`0.05n+0.10d=2.65`

Use the two equations above a system of linear equations to solve the variables n and d:

`\begin{gathered} n+d=31 \\ 0.05n+0.10d=2.65 \end{gathered}`

1. Solve n in the fist equation:

`\begin{gathered} n+d-d=31-d \\ \\ n=31-d \end{gathered}`

2. Use the value of n=31-d in the second equaiton:

`0.05(31-d)+0.10d=2.65`

3. Solve d:

`\begin{gathered} 1.55-0.05d+0.10d=2.65 \\ 1.55+0.05d=2.65 \\ 1.55-1.55+0.05d=2.65-1.55 \\ 0.05d=1.1 \\ (0.05)/(0.05)d=(1.1)/(0.05) \\ \\ d=22 \end{gathered}`

4. Use the value of d=22 to solve n:

`\begin{gathered} n=31-d \\ n=31-22 \\ n=9 \end{gathered}`

Then, you have 9 nickels and 22 dimes in your pocket