Question

Cameron has 21 coins in his pocket, all of which are dimes and quarters. If the total value of his change is315 cents, how many dimes and how many quarters does he have?

Answer 1

Given:

Cameron has 21 coins in his pocket, all of which are dimes and quarters.

Let, x be the number of quarters and y be the number of dimes.

The total cost is 315 cents.

The equations are,

`\begin{gathered} x+y=21\ldots\ldots\ldots\text{.}(1) \\ 25x+10y=315\ldots.\ldots\ldots....\ldots(2) \end{gathered}`

Solve the equation,

`\begin{gathered} x+y=21 \\ x=21-y\text{ put this value in equation (2)} \\ 25(21-y)+10y=315 \\ 525-25y+10y=315 \\ 525-315=15y \\ y=(210)/(15) \\ y=14 \end{gathered}`

Put the value of y in equation (1),

`\begin{gathered} x+y=21 \\ x+14=21 \\ x=21-14 \\ x=7 \end{gathered}`

Thus, the number of quarters are 7 and dimes are 14 .