Question

Rocco has 28 coins consisting of dimes and nickels. The coins are worth $2.60. How many nickels and dimes does he have?

Answer 1

See a solution process below:

Explanation:

First, let's give the number of nickels and dimes a name.

`n` will be the number of nickels Rocco has.

`d` will be the number of dimes Rocco has.

From the information in the problem we can write two equations:

`n + d = 28`

`0.05n + 0.10d = 2.60`

Step 1) Solve the first equation for `n`:

`n + d - color(red)(d) = 28 - color(red)(d)`

`n + 0 = 28 - d`

`n = 28 - d`

Step 2) Substitute `(28 - d)` for `n` in the second equation and solve for `d`:

`0.05n + 0.10d = 2.60` becomes:

`0.05(28 - d) + 0.10d = 2.60`

`(0.05 * 28) - (0.05 * d) + 0.10d = 2.60`

`1.4 - 0.05d + 0.10d = 2.60`

`1.4 + (-0.05 + 0.10)d = 2.60`

`1.4 + 0.05d = 2.60`

`-color(red)(1.4) + 1.4 + 0.05d = -color(red)(1.4) + 2.60`

`0 + 0.05d = 1.2`

`0.05d = 1.2`

`(0.05d)/color(red)(0.05) = 1.2/color(red)(0.05)`

`(color(red)(cancel(color(black)(0.05)))d)/cancel(color(red)(0.05)) = 22`

`d = 24`

Step 3) Substitute `24` for `d` in the solution to the first equation at the end of Step 1 and calculate `n`:

`n = 28 - d` becomes:

`n = 28 - 24`

`n = 4`

The Solution Is: Rocco has 24 dimes and 4 nickels