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If 2a = 3b, 1/3c = 6b^2, and b > 0, what is c in terms of a?

The answer choices are:
(A) 8a^2 + 6
(B) 8a^2 + 12
(C) 12a^2 + 6
(D) 18a^2 + 6
(E) 18a^2 + 12

Thank you!

  • Math -

    Actually, just did it again and got (D). However, it's an SAT question and I need the fastest way to solve it... what I did was plug in values for a and b (3 and 2, respectively) then find c (78) and plug a (3) back into each of the choices to see if c (78) and the answer were equal. Is there a faster way to do it?

  • Math -

    Start substituting:

    1/3c = 6b^2, so
    c = 18b^2

    Now, 3b=2a, so
    18b^2 = 2(3b)^2 = 2(2a)^2 = 8a^2

    I think you left out a +6 somewhere, since there are no such terms shown.

    Also, if a=3 and b=2, c=72, not 78, so it's a good sign something has been left out.

    So, if D is the answer, the question has been garbled. At any rate, you can see how I did it, so maybe you can apply the logic to the correct problem.

  • Math -

    Sorry- it was 1/3c = 6b^2 + 2.
    I can see your way of substituting, though!

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