# Math Help - Word Problems involving percents.

1. ## Word Problems involving percents.

Here is my problem:

What number increased by 6% of itself equals 2650?

I've gotton to the point of: 1.06x=2650 0VER 1.06(in a fraction). But I'm stuck on what to do next. Hellllp.

2. Originally Posted by Going Postal
Here is my problem:

What number increased by 6% of itself equals 2650?

I've gotton to the point of: 1.06x=2650 0VER 1.06(in a fraction). But I'm stuck on what to do next. Hellllp.

Let the number be $x$

$x + 6 \% x = 2650$

$\Rightarrow x + 0.06x = 2650$

$\Rightarrow 1.06x = 2650$ .......Now divide both sides by 1.06

$\Rightarrow x = \frac {2650}{1.06}$

$\Rightarrow x = 2500$

Note that "percentage" is just a fancy word for "over 100." so 6% means 6/100, 25% means 25/100. also note that "of" means "multiply." so 6% of x means 6/100 * x = 0.06 * x = 0.06x. and that's what we added to x

3. Well, let's call the number you're looking for $x$, as you did.

Then, notice that if you take $x$ and "add it to 6% of itself", you just get

$x + \{ \textrm{6\% of }x\} = x + 0.06 \times x = 1.06 \times x$

So your problem is just this:

$1.06 \times x = 2650$

so that $x = \frac{2650}{1.06} = 2500$

(Edit: My apologies, Jhevon was there first)

4. Ahhh. Mental errors. Might not would happen if my mom would get off my case. Thanks to both of you.