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A headphone manufacturer produces headphones at a cost of 60 dollars per headphone. What is the manufacturer's gross profit from selling 200 headphones if \frac{3}{5} of them are sold for 120 dollars each and the rest are sold for 140 dollars each?

Explanation	Calculations	Help
$We define R as the total number of headphones, N120 as the number sold at 120 dollars each, N140 as the number sold at 140 dollars each, Revenue as the total revenue, and Cost as the total cost.$	$R = 200$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate " \frac{3}{5} of them are sold for 120 dollars each" into a mathematical expression.$	$N_{120} = \frac{3}{5} \times R = \frac{3}{5} \times 200 = 120$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We subtract the number sold at 120 dollars each from the total to get the number sold at 140 dollars each.$	$N_{140} = R - N_{120} = 200 - 120 = 80$
$We translate "sold for 120 dollars each" and "sold for 140 dollars each" into revenue expressions and then sum them.$	$= 120 \times 120 + 140 \times 80= 25600$$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces headphones at a cost of 60 dollars per headphone" into a cost expression.$	$C os t = 60 \times R = 60 \times 200 = 12000$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate gross profit as revenue minus cost.$	$P ro f i t = R e v e n u e - C os t = 25600 - 12000 = 13600$	Theory & Tactics Method Card TRANS3-A Click to view full details

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B

A headphone manufacturer produces headphones at a cost of 60 dollars per headphone. What is the manufacturer's gross profit from selling 200 headphones if \frac{3}{5} of them are sold for 120 dollars each and the rest are sold for 140 dollars each?

Explanation	Calculations	Help
$We define R as the total number of headphones, N120 as the number sold at 120 dollars each, N140 as the number sold at 140 dollars each, Revenue as the total revenue, and Cost as the total cost.$	$R = 200$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate " \frac{3}{5} of them are sold for 120 dollars each" into a mathematical expression.$	$N_{120} = \frac{3}{5} \times R = \frac{3}{5} \times 200 = 120$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We subtract the number sold at 120 dollars each from the total to get the number sold at 140 dollars each.$	$N_{140} = R - N_{120} = 200 - 120 = 80$
$We translate "sold for 120 dollars each" and "sold for 140 dollars each" into revenue expressions and then sum them.$	$= 120 \times 120 + 140 \times 80= 25600$$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces headphones at a cost of 60 dollars per headphone" into a cost expression.$	$C os t = 60 \times R = 60 \times 200 = 12000$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate gross profit as revenue minus cost.$	$P ro f i t = R e v e n u e - C os t = 25600 - 12000 = 13600$	Theory & Tactics Method Card TRANS3-A Click to view full details

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B