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 $9900$.
$\frac{9900n}{9900}=\frac{-374625}{9900}$
$n=-\frac{1665}{44}$

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

Thanks!
-TetraFish