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A custom pen manufacturer produces 240 pens at a cost of 35 dollars per pen. What is the manufacturer's gross profit from the sale of all the pens if \frac{1}{3} of the pens are sold for 55 dollars per pen and the rest are sold for 70 dollars per pen?

Explanation	Calculations	Help
$We use P to represent the total number of pens.$	$P = 240$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate $\textbf{"\frac{1}{3} of the pens are sold for 55 dollars per pen"}$ into a mathematical expression to find the quantity sold at 55 dollars per pen.$	$N_{55} = \frac{1}{3} P N_{55} = \frac{1}{3} \times 240 N_{55} = 80$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the rest are sold for 70 dollars per pen" to find the quantity sold at 70 dollars per pen.$	$N_{70} = P - N_{55} N_{70} = 240 - 80 N_{70} = 160$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We translate "sold for 55 dollars per pen" and "sold for 70 dollars per pen" into revenue expressions and add them.$	$R e v e n u e = 55 \times N_{55} + 70 \times N_{70} R e v e n u e = 55 \times 80 + 70 \times 160 R e v e n u e = 4400 + 11200 R e v e n u e = 15600$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces pens at a cost of 35 dollars per pen" into a cost expression.$	$C os t = 35 \times P C os t = 35 \times 240 C os t = 8400$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate the gross profit using the profit formula.$	$P ro f i t = R e v e n u e - C os t P ro f i t = 15600 - 8400 P ro f i t = 7200$	Theory & Tactics Method Card TRANS3-A Click to view full details

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B

A custom pen manufacturer produces 240 pens at a cost of 35 dollars per pen. What is the manufacturer's gross profit from the sale of all the pens if \frac{1}{3} of the pens are sold for 55 dollars per pen and the rest are sold for 70 dollars per pen?

Explanation	Calculations	Help
$We use P to represent the total number of pens.$	$P = 240$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate $\textbf{"\frac{1}{3} of the pens are sold for 55 dollars per pen"}$ into a mathematical expression to find the quantity sold at 55 dollars per pen.$	$N_{55} = \frac{1}{3} P N_{55} = \frac{1}{3} \times 240 N_{55} = 80$	Theory & Tactics Method Card TRANS2-B Click to view full details
$We translate "the rest are sold for 70 dollars per pen" to find the quantity sold at 70 dollars per pen.$	$N_{70} = P - N_{55} N_{70} = 240 - 80 N_{70} = 160$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We translate "sold for 55 dollars per pen" and "sold for 70 dollars per pen" into revenue expressions and add them.$	$R e v e n u e = 55 \times N_{55} + 70 \times N_{70} R e v e n u e = 55 \times 80 + 70 \times 160 R e v e n u e = 4400 + 11200 R e v e n u e = 15600$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We translate "produces pens at a cost of 35 dollars per pen" into a cost expression.$	$C os t = 35 \times P C os t = 35 \times 240 C os t = 8400$	Theory & Tactics Method Card TRANS3-B Click to view full details
$We calculate the gross profit using the profit formula.$	$P ro f i t = R e v e n u e - C os t P ro f i t = 15600 - 8400 P ro f i t = 7200$	Theory & Tactics Method Card TRANS3-A Click to view full details

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B