Question

Asa saves dimes and quarters so that he will have exact change for he bus. He dabs and then dumps the container that he has been using for collecting his coins and finds he has 47 coins that are worth $9.50. How many of each coin does he have?

Answer 1

He have 32 quarters and 15 dimes.

Explanation:

Given:

Asa saves dimes and quarters so that he will have exact change for the bus.

He has 47 coins that are worth $9.50.

Now, to find the number of coin each he have.

Let the number of quarters be
`x.`

And the number of dimes be
`y.`

So, the total number of coins are:

`x+y=47.`

`y=47-x.`.........(1)

As given the total worth of coins = $9.50

And the value of a quarter = $0.25 and the value of a dime = $0.10.

Now, the total worth of coins are:

`0.25x+0.10y=9.50`

Putting the equation (1) in the place of
`y` we get:

`0.25x+0.10(47-x)=9.50`

`0.25x+4.7-0.10x=9.50`

`0.15x+4.7=9.50`

Subtracting both sides by 4.7 we get:

`0.15x=4.80`

Dividing both sides by 0.15 we get:

`x=32.`

The number of quarters = 32.

Now, putting the value of
`x` in equation (1) we get:

`y=47-32.`

`y=15.`

The number of dimes = 15.

Therefore, he have 32 quarters and 15 dimes.