runningguy wrote: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 trucks 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?
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3
This is a MIXTURE problem.
Revenue change for cars = -11%.
Revenue change for trucks = +7%.
Revenue change for the MIXTURE of cars and trucks = +1%.
The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.
Let C = car revenue and T = truck revenue.
Step 1: Plot the 3 percent changes on a number line, with the percent changes for C and T on the ends and the percent change for the mixture in the middle.
C -11%....................+1%....................+7% T
Step 2: Calculate the distances between the percentages.
C -11%.......
12.........+1%........
6.........+7% T
Step 3: Determine the ratio in the mixture.
The ratio of C to T is equal to the RECIPROCAL of the distances in red.
C:T = 6:12 = 1:2.
The correct answer is
A.
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