Question

You have a combined 132 pennies and nickels . The total value of the coins is $2.56. How many of each type of coin do you have?

Answer 1

Given:

The total number of coins, N=132.

The total value of coins, T=$2.56.

Let x be the number of pennies and y be the number of nickels.

Hence, the expression for the total number of coins can be written as,

`\begin{gathered} N=x+y \\ 132=x+y\text{ ---(1)} \end{gathered}`

We know,

`\begin{gathered} \text{100 penny=}1\text{ \$} \\ 1\text{ penny=}(1)/(100)\text{\$} \\ 1\text{ penny=}0.01\text{\$} \end{gathered}`

Also,

`\begin{gathered} 20\text{ nickels=1\$} \\ 1\text{ nickel=}(1)/(20)\text{ \$} \\ 1\text{ nickel=0.05 \$} \end{gathered}`

Since 1 penny=0.01 $ and 1 nickel =0.05$, the expression for the total value of coins can be written as,

`\begin{gathered} T=0.01x+0.05y \\ 2.56=0.01x+0.05y\text{ ---(2)} \end{gathered}`

Multiply equation (1) by 0.01.

`\begin{gathered} 132*0.01=0.01x+0.01y \\ 1.32=0.01x+0.01y\text{ ---(3)} \end{gathered}`

Subtract equation (3) from (2) and solve for y.

`\begin{gathered} 2.56-1.32=0.05y-0.01y \\ 1.24=0.04y \\ y=(1.24)/(0.04) \\ y=31 \end{gathered}`

So, y=31.

Now, put y=31 in equation (1) and solve for x.

`\begin{gathered} 132=x+31 \\ x=132-31 \\ x=101 \end{gathered}`

Therefore, the number of pennies is 101 and the number of nickels is 31.