Question

Sam has a jar contain 80 coins, all of which are either quarters or nickels. The total value of the coins is $14.60. How many of each type of coin does she have?

Answer 1

She have 53 type of quarters and 27 type of nickels.

Explanation:

Given:

Sam has a jar contain 80 coins, all of which are either quarters or nickels.

The total value of quarters and nickels is $14.60.

Now, to get each type of coin she have.

Let the number of quarters be
`x.`

And let the number of nickels be
`y.`

So, total number of coins:

`x+y=80`

`y=80-x\ \ \ ....(1)`

Now, the total value of coins:

`0.25(x)+0.05(y)=14.60`

Substituting the value of
`y` from equation (1):

`0.25(x)+0.05(80-x)=14.60`

`0.25x+4-0.05x=14.60`

`0.20x+4=14.60`

Subtracting both sides by 4 we get:

`0.20x=10.60`

Dividing both sides by 0.20 we get:

`x=53.`

The number of quarters = 53.

Now, to get the number of nickels by substituting the value of
`x` in equation (1):

`y=80-x\\\\y=80-53\\\\y=27.`

The number of nickels = 27.

Therefore, she have 53 type of quarters and 27 type of nickels.