Question

Madison collected a bunch of dimes and quarters for her school fundraiser. she collected a total of 122 coins and a total of $21.50. How many dimes and how many quarters did she collect?

Answer 1

Let:

x = number of dimes

y = number of quarters

She collected a total of 122 coins, so:

$x+y=122$

and a total of 21.50, so:

$0.1x+0.25y=21.50$

Let:

$\begin{gathered} x+y=122_{\text{ }}(1) \\ 0.1x+0.25y=21.50_{\text{ }}(2) \end{gathered}$

From (1):

$x=122-y_{\text{ }}(3)$

Replace (3) into (2):

$\begin{gathered} 0.1(122-y)+0.25y=21.50 \\ 12.2-0.1y+0.25y=21.50 \\ 0.15y=9.3 \\ y=\frac{9.3}{0.15} \\ y=62 \end{gathered}$

Replace the value of y into (3):

$\begin{gathered} x=122-62 \\ x=60 \end{gathered}$

She collected 60 dimes and 62 quarters