A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

This is a classic weighted average problem. I set up the equation: -11x + 7y = 1(x+y), where x and y are the 1996 revenues. Solving gives 12x = 6y, so x:y = 1:2. Answer A. Took me a minute to get the signs right.

I got confused by the wording: 'revenues from car sales in 1997 were down 11 percent from 1996' means if 1996 car revenue is C, then 1997 is 0.89C. Similarly trucks: 1.07T. Total 1997 is 1.01(C+T). Then 0.89C + 1.07T = 1.01C + 1.01T => 0.06T = 0.12C => C/T = 0.06/0.12 = 1/2. So ratio 1:2. But I initially set it up as C down 11% meaning C-0.11, which was wrong. Good learning.

Is there a faster way to do this? I tried plugging in the answer choices but got tangled. Maybe using alligation? The overall change is +1%, car is -11%, truck is +7%. The distances from 1% are 12 and 6, so ratio of car to truck is 6:12 = 1:2. That's quick!