Answer to Question #198451 in Algebra for Nicky

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

$\text{Cost of the bags is }C=R172,000\\\ \\ \text{She gained a profit of 24\% Profit} =172,000\times\dfrac{24}{100}=1720\times24=R \ 41,280$ 

$Sale \ price = Cost +Profit\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =R172,000+R41,280\\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =R213,280\\ \therefore Sale \ price = R 213,280\\ \ Discount \ given \ on \ sale \ price \ is \ 14\%\\ So, Let \ x \ be \ the \ tag \ price .\\ Since \ the \ discount \ 14\% \ is \ given \ on \ x,\\ So, the \ sale \ price =\dfrac{(100-14)}{100}\times x\\ \Rightarrow \dfrac{86}{100}\times x=213,280\\ \Rightarrow x=\dfrac{(213280\times 100)}{86}=248,000\\\ \\ \therefore The \ price\ tag \ \boxed{x=R 248,000}$