## 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