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Math help

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identify the percent of change as an increase or decrease. Then find the percent of change

Question 1     15 books to 21 books

Question 2      60 cars to 24 cars

Jan 30, 2018

#1
+1

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.

Jan 30, 2018

#1
+1

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.

TheXSquaredFactor Jan 30, 2018
#2
0

Thank you

Nerd123  Jan 30, 2018