A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment...

Question

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 costs 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?

GMAT Panda · Accepted Answer

20% We first create variables for the beginning-of-year costs S = salary costs at beginning of 1993 F = fringe-benefit costs at beginning of 1993 We translate the percent increases for each component "salary costs rose 3 percent" and "fringe-benefit costs rose 5.5 percent" 1.03S = S + 0.03S 1.055F = F + 0.055F We translate the overall percent increase "employment costs rose 3.5 percent" 1.035(S + F) = (S + F) + 0.035(S + F) We set the new total cost from components equal to the increased total cost 1.03S + 1.055F = 1.035(S + F) We expand and collect like terms to express fringe-benefit costs in terms of salary costs 1.03S + 1.055F = 1.035S + 1.035F 1.03S - 1.035S + 1.055F - 1.035F = 0 -0.005S + 0.020F = 0 0.020F = 0.005S We find the fraction of total costs represented by fringe benefits F/S = 0.005/0.020 = 0.25 F/S + F = F/S/S/S + F/S = 0.25/1 + 0.25 = 0.25/1.25 = 0.20 = 20%

Explanation	Calculations	Help
$We first create variables for the beginning-of-year costs$	$S = salary costs at beginning of 1993 F = fringe-benefit costs at beginning of 1993$
$We translate the percent increases for each component "salary costs rose 3 percent" and "fringe-benefit costs rose 5.5 percent"$	$1.03 S = S + 0.03 S 1.055 F = F + 0.055 F$
$We translate the overall percent increase "employment costs rose 3.5 percent"$	$1.035 (S + F) = (S + F) + 0.035 (S + F)$
$We set the new total cost from components equal to the increased total cost$	$1.03 S + 1.055 F = 1.035 (S + F)$
$We expand and collect like terms to express fringe-benefit costs in terms of salary costs$	$1.03 S + 1.055 F = 1.035 S + 1.035 F 1.03 S - 1.035 S + 1.055 F - 1.035 F = 0 - 0.005 S + 0.020 F = 0 0.020 F = 0.005 S$
$We find the fraction of total costs represented by fringe benefits$	$\frac{F}{S} = \frac{0.005}{0.020} = 0.25 \frac{F}{S + F} = \frac{F / S}{S / S + F / S} = \frac{0.25}{1 + 0.25} = \frac{0.25}{1.25} = 0.20 = 20%$

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