Question

There are 138 quarters and nickels in all. The combined value of the quarters and nickels is $34.50. How many quarters are there? What is the value of the nickels?

Answer 1

There 138 quarters and 0 nickels.

The value of nickels is $0.

Explanation:

A quarter is 0.25 of a dollar, and a nickel is 0.05 of a dollar. We are told that the total worth of nickels and dollars we have is 34.5, that is

`0.25q+0.05n=34.5`

where
`q` is the number of quarters, and
`n` is the number of nickels.

We are also told that total number of coins is 138, that is

`q+n=138`

so we have two equations:

`(1).\:0.25q+0.05n=34.5`

`(2).\:q+n=138`

To this system of equations we first solve for
`n` in second equation and substitute its value into the first equation:

`n=138-q`

the first equation becomes

`0.25q+0.05(138-q)=34.5`

`0.2q+6.9=34.5`

`\boxed{q=138}`

So we have 138 quarters.

Now we put this value into equation(2) and solve for
`n`

`n+138=138`

`\boxed{n=0}`

So we have 0 nickles and therefore their value is $0.