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QUESTION: Hello:

How would the following be solved?

[100% + ?%] X 30 = 36

Answer: 120%

100% X 30 = 30

+ ?% X 30 = 6

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100% + ?% X 30 = 36

What is 100% + ?%?

I thank you for your reply.

ANSWER: The % sign can be changed into a normal number by sliding the decimal two places.

For example, 13% = 0.13, 54% = 0.54, 130% = 1.30.

This means we can rewrite the problem as [1.00 + x] x 30 = 36.

Dividing both sides by 30 gives 1+x = 36/30.

Note that 36 is 6x6 and 30 is 5x6, so 36/30 = 6/5. This give 1 + x = 6/5.

Subtracting 1 from both sides gives x = 6/5 - 1.

Since 1 is the same as 5/5, that is x = 6/5 - 5/5 = (6-5)/5 = 1/5.

Since 10/5 = 2, 1/5 = 0.2, so x = 0.2.

To slide the decimal two places means we need to add a 0 and say that x = 0.20.

That can be converted back to a percent, so x = 20%.

When this is added to 100%, the result is 120%, and that is the answer.

When it is said that the answer is 120%, it must be asking for the value inside the [100% + ?%].

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for the reply!

I understand what you have explained but didn't you leave off the percent sign when you typed: [1.00 + x] x 30 = 36. ?

100% + ?% is [100/100 + ?/100]

I thank you again for your reply and explanation!

Yes, I left the percent sign out; x will come out to be 1/5, which is 20%.

And again, yes, 100% + ?% is [100/100 + ?/100].

Just remember when a percent sign is scene, it is the same as a number divided by 100.

Thus, 14% = 14/100 = 0.14, 132% = 1.32, -65% = -0.65, 1000% = 10, etc.

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