vikz_316 wrote:Hello, can anyone help me solve this question.
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?
1/2
4/5
1/1
3/2
5/3
We can solve this with a simple number line and an understanding of weighted averages.
-11 ------------------ 1 ---------- 7
In a system where two groups have equal weights, the average of the two groups is right in the middle.
In a system where the weights aren't equal, the average is always closer to the group with greater weight.
In this question, the weighted average is
twice as far (12 units) from cars as it is from trucks (6 units). Therefore, cars have
half the weight that trucks do and the ratio of cars:trucks is 1:2.
Let's look at some other examples to illustrate how we can quickly calculate ratios:
On a certain math test, the boys in a class averaged 60% and the girls averaged 80%. If the class average was 65%, what's the ratios of boys to girls in the class?
60 ----- 65 ------------------ 80
Here, the weighted average is 3 times as far from the girls as it is from the boys. Therefore, there are 1/3 as many girls as boys and the ratio of b:g is 3:1.
On a certain football team, the defensive players average 300lbs and the offensive players average 250lbs. If the average weight of all the players is 280 lbs, what's the ratio of the number of defensive players to offensive players?
250 ------------ 280 -------- 300
Here, the weighted average is 2/3 as far from the defensive players as it is from the offensive players. Therefore, there are 3/2 as many defensive players as offensive players and the ratio of D:O is 3:2.
