Math help

Question 1:

 

This question definitely suggests a percent increase since the number of books increased. In other words, 15 plus some percent of 15 equals 21 books. 

 

15 + some percent of 15 = 21

 

Let's let x = some percent because we do not know what that is. 

 

15 + x of 15 = 21

 

"Of" in mathematics means multiplication. 

 

15+15x=21

 

Now, solve for x:
 

\(15+15x=21\)	Now, isolate x in this equation.
\(15x=6\)	Divide by 15 from both sides.
\(x=\frac{6}{15}=\frac{2}{5}=0.4\)	Of course, we want to the percent increase, so we must convert 0.4, currently in decimal format, to a percent. To do that, just multiply by 100 and slap a percent sign behind the number.
\(x=0.4\Rightarrow 40\%\)	This, of course, is the increase.

 

Question 2:

 

The same concept can be used to calculate the percent decrease. I know that this problem involves that since the original amount is greater than the ending amount. 

 

60 cars - some percent of 60 cars =  24 cars

 

Let's let x equal some percent.

 

60 cars - x of 60 cars = 24 cars

 

As aforementioned, "of" is a direct indicator of multiplication in mathematics. 

 

60-60x=24

 

\(60-60x=24\)
\(-60x=-36\)	Divide by -60 on both sides.
\(x=\frac{-36}{-60}=\frac{3}{5}=0.6\)	Of course, this needs to be a percentage. Let's convert the answer into one.
\(x=0.6\Rightarrow 60\%\)	Remember that this is a decrease.

 

Note: I realize that I could have used the formula \(\frac{y_2-y_1}{y_1}*100\) to get the percent changed, but I think that the following methods allow you to understand what is occurring; the formula, on the other hand, does not.