Profit or Loss

A used car salesman sold two cars and received \$840 for each car. One of these transactions yielded a 40 percent profit for the dealer (compared to his purchase price), whereas the other amounted to a 25 percent loss. What is the dealer’s net profit (or loss) on the two transactions?
Source: NCTM Mathematics Teacher 2006

SOLUTION
Let p_1,p_2 represent the purchase prices of the cars. Suppose the dealer makes a profit on the first car and sustains a loss on the second car.
840-p_1=(40/100)p_1
Solve for p_1
840-p_1=(2/5)p_1
5(840-p_1)=2p_1
4200-5p_1=2p_1
4200=7p_1
p_1=600

p_2-840=(25/100)p_2
Solve for p_2
p_2-840=(1/4)p_2
4(p_2-840)=p_2
4p_2-3360=p_2
3p_2=3360
p_2=1120
Total purchase
600+1120=1720
Total sale
840+840=1680
Net loss
1720-1680=\$40

Answer: \$40 loss

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About mvtrinh

Retired high school math teacher.
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