Question

John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, `d`, in his pocket.?

Answer 1

`n = 4 + d`
`n + 2d = 25`

`d = 7`

Explanation:

In this case, you would not write an equation, you would write two equations. This will give you a system with two equations and two unknowns. The equations will be linearly independent, meaning you'll be able to use them to solve for `d`.

First, we know that John has four more nickels than dimes. Let `n` be the number of nickels and `d` the number of dimes. Then `n = 4+d` represents the relative amounts of nickels and dimes.

Additionally, we know that our change totals `$1.25`. Since dimes are worth 10 cents and nickels worth 5, this can be modeled with the equation `0.05n + 0.1d = 1.25`. To eliminate the decimals, we can multiply this through by 20 to yield `n + 2d = 25`.

We then have the two equations:
`n = 4 + d`
`n + 2d = 25`

We will substitute the first into the second, giving
`n + 2d = 25 -> (4+d) + 2d = 25 -> 3d = 21 -> d = 7`.

This gives us our answer; we have `7` dimes. (Plugging this value of `d` into the first equation also reveals that we have `11` nickels.)