Alexia earned 25% more at her new babysitting job than at her babysitting job. if she earned $30 more at her new babysitting job, find the amount she earned at her last babysitting job? ( show )

Breaking the problem down helps a lot! 
First let's write down the values we know an the values we need to know. 

Percent Increase of Pay: 25%
Increase of pay earned at the new job: $30
Amount earned from her last babysitting job: ? 

"If she earned $30 more at her new babysitting job..." This statement is stating that her raise (the 25% increase of pay) equals $30. It also states that 25% of her original pay is equal to $30. The reason isn't too hard to think of. Imagine if you were on the other side of this problem. Where you started with the original and you were told to find if she had a 25% increase what would you do? Take 25% of the number then add it to the original number. So in our case we are going backwards. If we have 25% of our 100% value we need to do the inverse operation that we did to obtain 25%. If you've done a bit of algebra and dabbled in things like solving for x and all that then this should be too hard. If not then I'll explain. 

25% of "N" = $30

Or you can think of it like this: 
25%*N = $30

To solve for "N" our original pay we need to get rid of the 25% that is multiplying our original pay. When something is multiplying a number you can remove it by dividing the number on BOTH sides. The reason why you divide it on both sides is because you need to keep the equation the same. (Dividing by the same number on both sides is equivalent to dividing by 1... so all the changes is the form, but it is still the same equation and is still equivalent)

So dividing 25% on both sides will look like this: 
(25%·N) / 25% = $30 / 25%

The 25% / 25% cancel out (meaning they equal 1... it's the same concept if say... you had 3/3... it's the same as saying you have 1)

So we are left with: 
N = $30 / 25%

From here we need to convert 25% into a number we can use. So let's convert it into the decimal equivalent. In order to do that we need to divide 25 by 100. So we are left with this: 

N = $30 / 0.25

If you can use a calculator then use it here. If not then I'll proceed. 0.25 is the same as 1/4. You can figure that out by turning it into a fraction which would be: 

25/100 simplified is 1/4. When you divide by a fraction you flip the fraction then multiply. So it looks like this now: 

$30 * 4 = $120

So our original pay was: $120