Question

How many solutions to 10n-0.375 = 0.1n -375 are there.

Answer 1

Hey!

First, let's write the problem.

`10n-0.375=0.1n-375`
Since we don't want any decimals, we will multiply both sides by
`1000`.

`10n\cdot \:1000-0.375\cdot \:1000=0.1n\cdot \:1000-375\cdot \:1000`

`10000n-375=100n-375000`
Add
`375` to both sides.

`10000n-375+375=100n-375000+375`

`10000n=100n-374625`
Subtract
`10n` from both sides.

`10000n-100n=100n-374625-100n`

`9900n=-374625`
Divide both sides by
`9900`.

`(9900n)/(9900)=(-374625)/(9900)`

`n=-(1665)/(44)`


`10n-0.375 = 0.1n -375` only has one solution

Thanks!
-TetraFish