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QUESTION: Hello:

How would the following answer be determined?

100% X 30 + ?% X 30 = 36

Or expressed as follows:

[100% + ?%] X 30 = 36

Answer: 120%

100% X 30 = 30

+ ?% X 30 = 6

-----------------

100% + ?% X 30 = 36

I thank you for your reply.

ANSWER: Hello,

Since 100% = 1, 100% x 30 = 1x30 = 30, and let the unknown be y

So... 100% X 30 + ?% X 30 = 36 ==> 30 + y%x30 = 36, subtracting 30 from both sides

gives: y%x30 = 6, now divide by 30 to get: y% = 6/30 ==> y% = 1/5 = 0.20, so y=20

So it is 20% (not 120%)

Abe

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

QUESTION: Hello:

Would this calculation make sense?

100% X 30 = 30

+ ?% X 30 = 6

-----------------

100% + ?% X 30 = 36

100/100 +?/100 X 30 = 36

1 + ?/100 X 30 = 36

1 + ?/100 = 36/30

1 + ?/100 = 1.2

?/100= 0.2 [Subtract 1 from both sides.]

? = 20 [Multiply both side by 100.]

Actually the 100% would not be necessary since it becomes "1".

100% X 30 + ?% X 30 = 36 equals 1 X 30 + ?% X 30 = 36 is the same as

30 + ?% X 30 = 36.

I thank you for your help and assistance.

Just make sure you use parentheses, as such:

100% X 30 = 30

+ ?% X 30 = 6

-----------------

(100% + ?%)X 30 = 36, let's use "x" instead of "?", so...

(1 + x/100)*30=36, using "*" for multiplication instead of "X"...divide by 30 to get

1+x/100=36/30 or 1+x/100=6/5, subtract 1 from both sides to get

x/100=1/5...then multiply by 100 to get x=20

Abe

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Comment | Thanks for the reply and comments! |

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Over 15 years teaching at the college level.**Organizations belong to**

NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.**Education/Credentials**

B.S. in Mathematics from Rensselaer Polytechnic Institute

M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook