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A toy manufacturer produces action figures at a cost of 12 dollars per figure. What is the manufacturer's gross profit from the sale of 180 figures if \frac{1}{4} of the figures are sold for 40 dollars per figure and the rest are sold for 60 dollars per figure?

Explanation	Calculations	Help
$We define R as the total number of figures produced, N_{40} as the number sold for 40 dollars each, and N_{60} as the number sold for 60 dollars each.$	$R = 180$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "1/4 of the figures are sold for 40 dollars per figure" into an expression for N_{40} .$	$N_{40} = \frac{1}{4} \times R = \frac{1}{4} \times 180 = 45$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We find the number sold at 60 dollars each by subtracting N_{40} from R .$	$N_{60} = R - N_{40} = 180 - 45 = 135$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We form the revenue expressions from "sold for 40 dollars per figure" and "sold for 60 dollars per figure", then add them.$	$R e v e n u e = 40 \times N_{40} + 60 \times N_{60} = 40 \times 45 + 60 \times 135 = 1800 + 8100 = 9900$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces action figures at a cost of 12 dollars per figure" into a cost expression.$	$C os t = 12 \times R = 12 \times 180 = 2160$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate gross profit by subtracting cost from revenue.$	$P ro f i t = R e v e n u e - C os t = 9900 - 2160 = 7740$	Theory & Tactics Method Card TRANS3-A Click to view full details

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B

A toy manufacturer produces action figures at a cost of 12 dollars per figure. What is the manufacturer's gross profit from the sale of 180 figures if \frac{1}{4} of the figures are sold for 40 dollars per figure and the rest are sold for 60 dollars per figure?

Explanation	Calculations	Help
$We define R as the total number of figures produced, N_{40} as the number sold for 40 dollars each, and N_{60} as the number sold for 60 dollars each.$	$R = 180$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "1/4 of the figures are sold for 40 dollars per figure" into an expression for N_{40} .$	$N_{40} = \frac{1}{4} \times R = \frac{1}{4} \times 180 = 45$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We find the number sold at 60 dollars each by subtracting N_{40} from R .$	$N_{60} = R - N_{40} = 180 - 45 = 135$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We form the revenue expressions from "sold for 40 dollars per figure" and "sold for 60 dollars per figure", then add them.$	$R e v e n u e = 40 \times N_{40} + 60 \times N_{60} = 40 \times 45 + 60 \times 135 = 1800 + 8100 = 9900$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces action figures at a cost of 12 dollars per figure" into a cost expression.$	$C os t = 12 \times R = 12 \times 180 = 2160$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate gross profit by subtracting cost from revenue.$	$P ro f i t = R e v e n u e - C os t = 9900 - 2160 = 7740$	Theory & Tactics Method Card TRANS3-A Click to view full details

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B