If (a + 12b)/4b = 18/5, which of the following can be determined?
I: a/b
II: 5b/(a + 7b)
III: (a + 3)/(b + 5)
(a + 12b)/4b = 18/5.
Cross-multiplying, we get:
5a + 60b = 72b
5a = 12b
a/b = 12/5.
I: a/b
a/b = 12/5.
The value of I can be determined.
To evaluate II and III, test TWO CASES.
II: 5b/(a + 7b)
Case 1: a=12, b=5
In this case, 5b/(a + 7b) = (5*5)/(12 + 7*5) = 25/47.
Case 2: a=24, b=10
In this case, 5b/(a + 7b) = (5*10)/(24 + 7*10) = 50/94 = 25/47.
Since in each case the result is the same -- 25/47 -- the value of II can be determined.
III: (a + 3)/(b + 5)
Case 1: a=12, b=5
In this case, (a + 3)/(b + 5) = (12+3)/(5+5) = 15/10 = 3/2.
Case 2: a=24, b=10
In this case, (a + 3)/(b + 5) = (24+3)/(10+5) = 27/15 = 9/5.
Since the result is NOT the same in each case, the value of III cannot be determined.
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