truck & car word problem

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truck & car word problem

by ska7945 » Tue Aug 12, 2008 6:15 am
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?
A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3

provide your reasoning please.
Answer : A
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by santa_dem » Tue Aug 12, 2008 6:34 am
the number of cars and trucks sold in 1997, based on the 1996 numbers is:

x*(100%-11%)+y*(100%+7%)=(x+y)*(100%+1%)

where x - cars sold in 1996 and y - trucks sold in 1996.

x*89%+y*107%=x*101%+y*101%

y*(107%-101%)=x*(101%-89%)

y*6%=x*12%

x/y=6%/12%=1/2

Answer A.