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# Basic Math/100% X 30 + ?% X 30 = 36

Question
QUESTION: Hello:

How would the following answer be determined?

100% X 30 + ?% X 30 = 36

Or expressed as follows:

[100% + ?%] X 30 = 36

100% X 30 = 30
+ ?% X 30 =  6
-----------------
100% + ?% X 30 = 36

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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Basic Math

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#### Abe Mantell

##### Expertise

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!

##### Experience

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