Question

Thomas has a collection of 25 coins some are dimes and some are quarters. If the total value of all the coins is $5.05, how many of each kind of coin are there?

Answer 1

Thomas has 8 dimes and 17 quarters

Explanation:

To start, let's call the number of dimes Thomas has `d` and the number of quarters he has `q`.

Then, because we know he has 25 coins we can write:

`d + q = 25`

We also know the combination of dimes and quarters add up to `$5.05` so we can also write:

`0.10d + 0.25q = 5.05`

Solving the first equation for `q` gives:

`d + q - d = 25 - d`

`q = 25 - d`

We can now substitute `25 - d` for `q` in the second equation and solve for `d`:

`0.10d + 0.25(25 - d) = 5.05`

`0.10d + 6.25 - 0.25d = 5.05`

`6.25 - 0.15d = 5.05`

`6.25 - 0.15d + 0.15d - 5.05 = 5.05 + 0.15d - 5.05`

`1.20 = 0.15d`

`1.20/0.15 = (0.15d)/0.15`

`d = 8`

We can now substitute `8` for `d` in the solution of the first equation and calculate `q`.

`q = 25 - 8`

`q = 17`