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A-dealer-sold-a-car-to-a-man-and-made-a-profit-of-15-the-man-then-sold-it-to-a-woman-for-120-175-00-at-a-loss-of-5-How-much-did-the-dealer-buy-the-car-




Question Number 7901 by tawakalitu last updated on 24/Sep/16
A dealer sold a car to a man and made a profit of 15%  the man then sold it to a woman for #120,175.00  at a loss of 5%. How much did the dealer buy the car.
$${A}\:{dealer}\:{sold}\:{a}\:{car}\:{to}\:{a}\:{man}\:{and}\:{made}\:{a}\:{profit}\:{of}\:\mathrm{15\%} \\ $$$${the}\:{man}\:{then}\:{sold}\:{it}\:{to}\:{a}\:{woman}\:{for}\:#\mathrm{120},\mathrm{175}.\mathrm{00} \\ $$$${at}\:{a}\:{loss}\:{of}\:\mathrm{5\%}.\:{How}\:{much}\:{did}\:{the}\:{dealer}\:{buy}\:{the}\:{car}. \\ $$
Answered by sandy_suhendra last updated on 24/Sep/16
the man buys the car = ((100)/(95))×120,175= 126,500 =the dealer sold  the dealer buys = ((100)/(115))×126,500 = 110,000
$${the}\:{man}\:{buys}\:{the}\:{car}\:=\:\frac{\mathrm{100}}{\mathrm{95}}×\mathrm{120},\mathrm{175}=\:\mathrm{126},\mathrm{500}\:={the}\:{dealer}\:{sold} \\ $$$${the}\:{dealer}\:{buys}\:=\:\frac{\mathrm{100}}{\mathrm{115}}×\mathrm{126},\mathrm{500}\:=\:\mathrm{110},\mathrm{000} \\ $$$$ \\ $$
Commented by tawakalitu last updated on 24/Sep/16
thanks for your help
$${thanks}\:{for}\:{your}\:{help} \\ $$
Answered by Rasheed Soomro last updated on 24/Sep/16
Let the dealer bought the car in x  Dealer sold the car    x+15% of x                                           =x+((15)/(100))×x=x+((3x)/(20))=((23x)/(20))  The man bought the car in  ((23x)/(20))  He sold the car at 5% loss:  ((23x)/(20))−((23x)/(20))×(5/(100))=((23x)/(20))−((23x)/(400))                                                           =((460x−23x)/(400))=((437x)/(400))  He sold the car for #120,175.00  So,                                    ((437x)/(400))=120,175                                                          x=((120175×400)/(437))=110000  The dealer bought the car in 110,000
$${Let}\:{the}\:{dealer}\:{bought}\:{the}\:{car}\:{in}\:{x} \\ $$$${Dealer}\:{sold}\:{the}\:{car}\:\:\:\:{x}+\mathrm{15\%}\:{of}\:{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={x}+\frac{\mathrm{15}}{\mathrm{100}}×{x}={x}+\frac{\mathrm{3}{x}}{\mathrm{20}}=\frac{\mathrm{23}{x}}{\mathrm{20}} \\ $$$${The}\:{man}\:{bought}\:{the}\:{car}\:{in}\:\:\frac{\mathrm{23}{x}}{\mathrm{20}} \\ $$$${He}\:{sold}\:{the}\:{car}\:{at}\:\mathrm{5\%}\:{loss}:\:\:\frac{\mathrm{23}{x}}{\mathrm{20}}−\frac{\mathrm{23}{x}}{\mathrm{20}}×\frac{\mathrm{5}}{\mathrm{100}}=\frac{\mathrm{23}{x}}{\mathrm{20}}−\frac{\mathrm{23}{x}}{\mathrm{400}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{460}{x}−\mathrm{23}{x}}{\mathrm{400}}=\frac{\mathrm{437}{x}}{\mathrm{400}} \\ $$$${He}\:{sold}\:{the}\:{car}\:{for}\:#\mathrm{120},\mathrm{175}.\mathrm{00} \\ $$$${So},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{437}{x}}{\mathrm{400}}=\mathrm{120},\mathrm{175}\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{120175}×\mathrm{400}}{\mathrm{437}}=\mathrm{110000} \\ $$$${The}\:{dealer}\:{bought}\:{the}\:{car}\:{in}\:\mathrm{110},\mathrm{000} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$
Commented by tawakalitu last updated on 24/Sep/16
thanks so much. i appreciate.
$${thanks}\:{so}\:{much}.\:{i}\:{appreciate}. \\ $$

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