Question

You have a total of 21 coins, all nickels and dimes. The total value is $1.70. How many nickels and how many dimes do you have?

Answer 1

The number of nickels is `8` and the number of dimes is `13`.

Explanation:

Representing the nickels as `n` and the dimes as `d`, and knowing that a nickel is `5` cents and a dime is `10` cents, we can write two equations from the given data.

1. `n+d=21`
2. `5n+10d=170`

We use the first equation to derive a value for `n`.

`n+d=21`

Subtract `d` from each side.

`n+d-d=21-d`

`n=21-d`

We now simplify the second equation by dividing all terms by `5`.

`5n+10d=170`

`(5n)/5+(10d)/5=170/5`

`(1cancel5n)/(1cancel5)+(2cancel10d)/5=(34cancel170)/(1cancel5)`

`n+2d=34`

Using the value for `n` from the first equation, substitute `n` with `color(red)((21-d))` in the simplified second equation.

`n+2d=34`

`color(red)((21-d))+2d=34`

Open the brackets and simplify.

`21-d+2d=34`

`21+d=34`

Subtract `21` from each side.

`21-21+d=34-21`

`d=13`

In the first equation, substitute `d` with `color(blue)(13)`.

`n+d=21`

`n+color(blue)13=21`

Subtract `13` from each side.

`n+13-13=21-13`

`n=8`

Thus, the number of nickels is `8` and the number of dimes is `13`.