Chapter 6.1, Problem 56PFA

To determine

To find: The number of dimes.

Answer to Problem 56PFA

4

Explanation of Solution

Given information:

There are a quarter, some dimes and some nickels.

Calculation:

Let there be x dimes and y nickels.

Then, the system of equations becomes:

  $\begin{array}{l}0.25+0.10x+0.05y=1\\ 1+x+y=12\end{array}$

Then,

  $\begin{array}{l}25+0.10x+0.05y=1\\ 0.10x+0.05y=0.75\end{array}$

And,

  $\begin{array}{l}1+x+y=12\\ x+y=11\end{array}$

So, the final system of equations becomes:

  $\begin{array}{l}0.10x+0.05y=0.75\\ x+y=11\end{array}$

Solve the system to get the solution as follows:

  $x=4,y=7$ .

So, there are 4 dimes.