Lester has sold 72 Christmas cards and has collected 404 If

Lester has sold 72 Christmas cards and has collected $4.04. If he charged 5 cents each for one kind and 7 cents each for all the others, how many of each kind did he sell? Please explain the calculation.

Solution

Let the numbers of the Christmas cards sold by Lester , costing $0.05 be x.Then the number of the Christmas cards sold by Lester , costing $0.07 is 72-x ( as the total number of Christmas cards sold is 72). Further, the sale price of these cards is 0.05* x + (72-x)*0.07= 0.05x + 5.04 -0.07 x = 5.04 -0.02 x. Now, since Lester has collected $ 4.04, therefore, 4.04 = 5.04 -0.02 x or, 0.02cx = 5.04 -0.04 = 1 so that x = 1/0.02 = 50. Then 72-x = 72-50 = 22. Thus Lester has sold 50 Christmas cards costing 5 cents each and 22 Christmas cards costing 7 cents each. Since 50*0.05 + 22 *0.07 = 2.50 + 1.54 = 4.04, our answer is correct.