Answer to Question #185734 in Algebra for NN HLONGWANE

Question

A merchant purchased a line of handbags for R172,00 each. She wants to offer a 14% discount off the listed

selling price and still make a 24% profit. The price that she should mark on the label is

Answer 1

$Cost \ of \ the \ bags \ is \ C=R172,000\\ She \ gained \ a \ profit \ of \ 24\%\Rightarrow Profit =172,000*\frac{24}{100}=1720*24=R$ 41,280$Sale \ price = Cost +Profit\\ =R172,000+R41,280\\ =R213,280\\ Sale \ price = R 213,280\\ Discount \ given \ on \ sale \ price \ is 14\%\\ Let \ 'x' \ be \ the \ tag \ price .\\ Since \ the \ discount \ 14\% \ is \ given \ on \ x,\\ the \ sale \ price =\frac{(100-14)}{100}*x\\ \Rightarrow \frac{86}{100}*x=213,280\\ \Rightarrow x=\frac{(213280*100)}{86}=248,000\\ \therefore The \ price\ tag \ x=R 248,000$