Question

You have a combined 26 dimes and quartersThe total value of the coins is $5.45. How many of each type of coin do you have

Answer 1

Answer: There are;

7 Dimes and 19 Quarters

$\begin{gathered} x=7 \\ y=19 \end{gathered}$

Explanation:

Let x and y represent the number of each type of dime and quarter you have respectively.

Given that you have a combined 26 dimes and quarters.

$x+y=26\text{ ------ 1}$

Also, recall that;

$\begin{gathered} 1\text{ dime = \ 0.10} \\ 1\text{ quarter = \ 0.25} \end{gathered}$

Given that the total value of the coins is $5.45.

$0.10x+0.25y=5.45\text{ -------- 2}$

Solving the set equations.

multiplying equation 2 by 4;

and subtract from equation 1.

$\begin{gathered} 0.10x+0.25y=5.45\text{ -------- 2} \\ \times4 \\ = \\ 0.40x+y=21.8 \\ \\ x+y=26 \\ - \\ 0.40x+y=21.8 \\ = \\ 0.60x+0=4.2 \\ x=\frac{4.2}{0.6} \\ x=7 \end{gathered}$

so, we can substitute the value of x into equation 1 to get y;

$\begin{gathered} 7+y=26 \\ y=26-7 \\ y=19 \end{gathered}$

Therefore, there are;

7 Dimes and 19 Quarters

$\begin{gathered} x=7 \\ y=19 \end{gathered}$