If 3(4x+5π)=P, then 6(8x+10π)=

1992 AMC 12 Problem 1

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3(4x+5\pi)=P,

then

6(8x+10\pi)=

2P

4P

6P

8P

18P

Compare

8x+10\pi

with

4x+5\pi

Account separately for the change inside the parentheses and the change in the outside coefficient

We have

8x+10\pi=2(4x+5\pi),

\begin{gathered} 6(8x+10\pi)\\ {}=12(4x+5\pi)\\ {}=4\bigl[3(4x+5\pi)\bigr]\\ {}=4P. \end{gathered}

Thus the correct answer is B.