Math CentralQuandaries & Queries


Question from JAMES, a student:

A businessman bought a number of similar articles for a total of sh. 6000. Three of the articles turned out to be defective with no resale value. He sold the remaining articles at 12.5% each above the cost price making a total profit of sh 480. How many articles had he bought?

James, there are two numbers missing, the number of articles purchased and the cost of each item. I am going to let $n$ be the number if items her purchased and sc $c$ the cost of each item he purchased. His total cost was sh 6000 and hence

\[n \times c = 600.\]

He sold all the non-defective items so how many did he sell? He sold the items at 12.5% above his cost price so what was the selling price of each item? His revenue was his cost plus his profit so his revenue was sh $600 + 480 = 6480.$ Use these facts to write a second equation involving $n$ and $c$ and then solve for $n.$


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