Question

Solve: Eight coins (dimes and quarters) are worth 170 cents. How many dimes are there? _____

Answer 1

Explanation

To solve the question, we have to convert the coins the same units

A dime is worth 10 cents. A quarter is worth 25 cents.

So we will have

Let dimes be d

Let quarter be q

Since there are 8 coins

Then

`d+q=8`

Also

`0.1d+0.25q=1.7`

So we can now solve the equations as follow

`\mathrm{Substitute\:}d=8-q`

`\begin{gathered} \begin{bmatrix}0.1\left(8-q\right)+0.25q=1.7\end{bmatrix} \\ \\ \begin{bmatrix}0.8+0.15q=1.7\end{bmatrix} \\ \\ q=6 \end{gathered}`

Next, we will have to get d

`\begin{gathered} d=8-q \\ d=8-6=2 \\ d=2 \end{gathered}`

Therefore, there are 2 dimes