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Post subject: GMAT Functions Posted: Tue Sep 07, 2010 3:49 am 

Joined: Sun May 30, 2010 3:15 am Posts: 424

Suppose the number of fans at a baseball game is given by the function b(x) = 150x – 6 and the number of fans at football game is given by f(b) = 2b + 12. What is the value of x when there are 1200 fans at the football game? A. 2 B. 5 C. 4 D. 3 E. 7
(C) The first thing to do is to substitute f = 1200 into the second equation to solve for b: b = (f – 12)/2 = (1200 – 12)/2 = 1188/2 = 594.
Now, we substitute b = 594 into the first equation to solve for x: x = (b + 6)/150 = (594 + 6)/150 = 4.
The correct answer is C. 
I'm totally stuck on how you get to b = (f – 12)/2, can you elaborate a little more? Thanks.


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Gennadiy

Post subject: Re: math (test 2, question 18): algebra Posted: Tue Sep 07, 2010 4:01 am 

Joined: Sun May 30, 2010 2:23 am Posts: 498

When we substitute f = 1200 into the second formula:
f(b) = 2b + 12
we get equation:
1200 = 2b + 12
and solve it for b:
b = (1200 – 12)/2 b = 594 
We could also solve for b first and then plug in f = 1200. (As it is done in question explanation). NOTE that for simplicity we use denotation f instead of f(b).
f(b) = 2b + 12 f = 2b + 12 f – 12 = 2b b = (f – 12)/2


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