Question

Lily has $2.75 in her pocket, consisting of dimes and quarters. If there are 17 coins in all, how many of each does she have?

Answer 1

There are 10 dimes and 7 quarters of coins in all she have.

Explanation:

Given:

Lily has $2.75 in her pocket, consisting of dimes and quarters.

There are 17 coins in all.

Now, to find the number of coins each she have.

Let the dimes be
`x.`

And the quarters be
`y.`

So, the total number of coins:

`x+y=17.`.......(1)

`x=17-y.`

The value of a dime = $0.10.

And the value of a quarter = $0.25.

Now, the total money Lily has in her pocket:

`0.10x+0.25y=2.75.`

Putting the value in the place of
`x` we get:

`0.10(17-y)+0.25y=2.75`

⇒
`1.7-0.10y+0.25y=2.75`

⇒
`1.7+0.15y=2.75`

Subtracting both sides by 1.7 we get:

⇒
`0.15y=1.05`

Dividing both sides by 0.15 we get:

⇒
`y=7.`

The number of quarters = 7.

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

`x+y=17.`

`x+7=17.`

Subtracting both sides by 7 we get:

⇒
`x=10.`

The number of dimes = 10.

Therefore, there are 10 dimes and 7 quarters of coins in all she have.