1. ## Advanced Percentage Problems

1. a is what percent of b?

2. What percent of a is 5?

3. 20 is what percent more than 15?

4. 2/5 is what percent of b?

5. 15 is what percent less than 20?

6. 1/2 is what percent more than 1/5?

7. 2/3 is what percent less than 1 1/2?

8. If a>b, what percent more than b is a?

9. if a<b, what percent less than b is a?

10. What is 40% more than 20%?

11. What is 40% more than 20% of 40?

12. What is 40% more than 40 less than 20% of 80?

13. What is a% less than b% more than c?

2. Where is your work? Help me understand the trouble you are having by seeing what you are doing wrong.

3. For percent problems I find it helpful to use this mnemonic:

$\frac{percent}{100} = \frac{is}{of}$

What you do is you substitute numbers next to the words above into the proportion. So, for example:

1. a is what percent of b?
Substitute a for the "is", a variable for "percent", and b for "of".

$\frac{x}{100} = \frac{a}{b}$

$x = \frac{100a}{b}$

So a is $\frac{100a}{b}$ percent of b.

2. What percent of a is 5?
Substitute 5 for the "is", a variable for "percent", and a for "of".

$\frac{x}{100} = \frac{5}{a}$

$x = \frac{500}{a}$

So $\frac{500}{a}$ percent of a is 5.

3. 20 is what percent more than 15?
20 is 5 more than 15, so this is also asking "5 is what percent of 15?" Substitute 5 for the "is", a variable for "percent", and 15 for "of".

$\frac{x}{100} = \frac{5}{15}$

$x = \frac{100}{3}$

x = 33.33...%

So 20 is 33.33...% more than 15.

That's all from me. You try the rest. Good luck!

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4. I don't get anything. I mean, I don't how to do anything like these?

5. you can say: let $a$ is $x\%$ of $b$

so $a=\frac{x}{100}\cdot b$

so $\frac{a}{b}=\frac{x}{100}$

or $x=\frac{100a}{b}$

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# advance maths for percentage

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