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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?

Explanation	Calculations	Help
$We first create variables for the beginning-of-year costs$	$S = salary costs at beginning of 1993 F = fringe-benefit costs at beginning of 1993$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the percent increases for each component "salary costs rose 3 percent" and "fringe-benefit costs rose 5.5 percent"$	$1.03 S = S + 0.03 S 1.055 F = F + 0.055 F$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate the overall percent increase "employment costs rose 3.5 percent"$	$1.035 (S + F) = (S + F) + 0.035 (S + F)$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We set the new total cost from components equal to the increased total cost$	$1.03 S + 1.055 F = 1.035 (S + F)$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We expand and collect like terms to express fringe-benefit costs in terms of salary costs$	$1.03 S + 1.055 F = 1.035 S + 1.035 F 1.03 S - 1.035 S + 1.055 F - 1.035 F = 0 - 0.005 S + 0.020 F = 0 0.020 F = 0.005 S$
$We find the fraction of total costs represented by fringe benefits$	$\frac{F}{S} = \frac{0.005}{0.020} = 0.25 \frac{F}{S + F} = \frac{F / S}{S / S + F / S} = \frac{0.25}{1 + 0.25} = \frac{0.25}{1.25} = 0.20 = 20%$	Theory & Tactics Method Card FDPR2-A Click to view full details

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20%

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?

Explanation	Calculations	Help
$We first create variables for the beginning-of-year costs$	$S = salary costs at beginning of 1993 F = fringe-benefit costs at beginning of 1993$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the percent increases for each component "salary costs rose 3 percent" and "fringe-benefit costs rose 5.5 percent"$	$1.03 S = S + 0.03 S 1.055 F = F + 0.055 F$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate the overall percent increase "employment costs rose 3.5 percent"$	$1.035 (S + F) = (S + F) + 0.035 (S + F)$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We set the new total cost from components equal to the increased total cost$	$1.03 S + 1.055 F = 1.035 (S + F)$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We expand and collect like terms to express fringe-benefit costs in terms of salary costs$	$1.03 S + 1.055 F = 1.035 S + 1.035 F 1.03 S - 1.035 S + 1.055 F - 1.035 F = 0 - 0.005 S + 0.020 F = 0 0.020 F = 0.005 S$
$We find the fraction of total costs represented by fringe benefits$	$\frac{F}{S} = \frac{0.005}{0.020} = 0.25 \frac{F}{S + F} = \frac{F / S}{S / S + F / S} = \frac{0.25}{1 + 0.25} = \frac{0.25}{1.25} = 0.20 = 20%$	Theory & Tactics Method Card FDPR2-A Click to view full details

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20%