basso25@ wrote:
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary cost rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?
A) 16.5%
B) 20%
C) 35%
D) 55%
E) 65%
This is a MIXTURE problem:
Increase in salary costs = 3%.
Increase in fringe-benefit costs = 5.5%.
Increase in the cost of the MIXTURE (salaries + fringe-benefits) = 3.5%.
Use ALLIGATION -- a very good way to handle MIXTURE PROBLEMS.
Let S = the increase in salary costs and F = the increase in fringe-benefit costs.
Step 1: Plot the 3 percentages on a number line, with the percentages attributed to the two ingredients (3% and 5.5%) on the ends and the percentage attributed to the mixture (3.5%) in the middle.
S 3%----------3.5%-----------F 5.5%
Step 2: Calculate the distances between the percentages.
S 3%----
.5----3.5%-----
2----F 5.5%
Step 3: Determine the ratio in the mixture.
The ratio of S to F in the mixture is the RECIPROCAL of the distances in red.
S:F = 2 : .5 = 4:1.
Since S:F = 4:1, and 4+1=5, of every $5 spent, $4 was spent on salaries and $1 was spent on fringe benefits.
Thus:
F/total = 1/5 = 20%.
The correct answer is
B.
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