Question

mayelle earns $18000 a year. After a raise, she earns $19500. Find the percent change and if it’s a decrease or increase

Answer 1

Ok, it's all pretty much like the "$50 coat is on sale for $35". 

If the regular price of the coat is $50 and now it is on sale for $35, then it will cost you $15 less, like this: 
$50 - $35 = $15 

You could also say the coat was discounted by $15, or the coat was reduced by $15, or you'll save $15 if you buy that coat ($50 - $15 = 35). 

You could also put it in terms of percentages. If the discount is $15, you can figure that $15 is what percent of the regular price, like this: 
$15 = X% of $50 
$15 = X% x $50 (divide both sides by 50 to isolate X) 
15/50 = X% 
.30 = X% (multiply by 100 to convert to a non-decimal) 
30% = X 

So, you can say all of the following and they all mean the same thing: 
1. the $50 coat is on sale for $35 
2. the $50 coat is discounted by $15 
3. the $50 coat is reduced by $15 
4. you'll save $15 if you buy this coat 
5. the $50 coat is on sale for 30% off 
6. the $50 coat is discounted by 30% 
7. you'll save 30% if you buy this coat 
8. 30% savings! 
9. Save 30%! 

So, how does that apply to the $18,000 a year? Ok, if Shelby earns $18,000 this year and then earns $19,500 next year, then she gets an additional $1,500 ($19,500 - $18,000 = $1,500). In the coat problem, everything was discounted, on sale, going down. In this problem, everything is going up, increasing. 

You know the dollar increase is $1,500. To figure the percent increase, you need to figure out that $1,500 is what % of $18,000. Remember, it's not the $19,500 that was increased; it was an increase on the $18,000: 
$1,500 = X% of $18,000 
1,500/18,000 = X% 
.083333 = X% 
8.3333% = X 

One more: If Shelby get a 10% increase in her salary at the end of one year, that's the same as saying that Shelby gets her salary plus she gets 10% more, like this: 

$18,000 + (10% of $18,000) = 
$18,000 + $1,800 = 
$19,800 end of first year 

For the second year, her salary begins at $19,800 and increases 10%, like this: 
$19,800 + (10% x $19,800) = 
$19,800 + $1,980 = 
$21,780 end of second year 

You can do it from here.

Answer 2

It has an increase of 1,500 or 8.33%.