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A rug manufacturer produces rugs at a cost of 75USD per rug. What is the manufacturer's gross profit from the sale of 150 rugs if \frac{2}{3} of the rugs are sold for 150USD per rug and the rest are sold for 200USD per rug?

Explanation	Calculations	Help
$We define variables to represent each quantity:$	$R, N_{150}, N_{200}, R e v e n u e, C os t, P ro f i t$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "2/3 of the rugs are sold for 150USD per rug" to find the number sold at 150USD.$	$N_{150} = \frac{2}{3} R = \frac{2}{3} \times 150 = 100$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We find the number sold at 200USD by subtracting the number sold at 150USD from the total.$	$N_{200} = R - N_{150} = 150 - 100 = 50$
$We translate "sold for 150USD per rug" and "sold for 200USD per rug" into revenue expressions and sum them using the revenue formula.$	$R e v e n u e = 150 \times N_{150} + 200 \times N_{200} = 150 \times 100 + 200 \times 50 = 15000 + 10000 = 25000$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces rugs at a cost of 75USD per rug" into a cost expression using the cost formula.$	$C os t = 75 \times R = 75 \times 150 = 11250$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate gross profit by applying Profit = Revenue - Cost .$	$P ro f i t = R e v e n u e - C os t = 25000 - 11250 = 13750$	Theory & Tactics Method Card TRANS3-A Click to view full details

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13,750 USD (Option C)

A rug manufacturer produces rugs at a cost of 75USD per rug. What is the manufacturer's gross profit from the sale of 150 rugs if \frac{2}{3} of the rugs are sold for 150USD per rug and the rest are sold for 200USD per rug?

Explanation	Calculations	Help
$We define variables to represent each quantity:$	$R, N_{150}, N_{200}, R e v e n u e, C os t, P ro f i t$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "2/3 of the rugs are sold for 150USD per rug" to find the number sold at 150USD.$	$N_{150} = \frac{2}{3} R = \frac{2}{3} \times 150 = 100$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We find the number sold at 200USD by subtracting the number sold at 150USD from the total.$	$N_{200} = R - N_{150} = 150 - 100 = 50$
$We translate "sold for 150USD per rug" and "sold for 200USD per rug" into revenue expressions and sum them using the revenue formula.$	$R e v e n u e = 150 \times N_{150} + 200 \times N_{200} = 150 \times 100 + 200 \times 50 = 15000 + 10000 = 25000$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces rugs at a cost of 75USD per rug" into a cost expression using the cost formula.$	$C os t = 75 \times R = 75 \times 150 = 11250$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate gross profit by applying Profit = Revenue - Cost .$	$P ro f i t = R e v e n u e - C os t = 25000 - 11250 = 13750$	Theory & Tactics Method Card TRANS3-A Click to view full details

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13,750 USD (Option C)