Name: Travis
Who is asking: Student
Level: Middle

An art teacher buys exactly 100 items at this sale, and the total cost before tax is $100. She buys at least one of each item. How many of each item does she buy?

Markers $0.50
Sketch Pads $3.00
Paint Sets $10.00

Hi Travis,

Let M stand for Markers, S for Sketch pads & P for Paint Sets. You have M, S, P > 0;

M+S+P = 100;
(1/2)M+3S+10P = 100.

Subtract the first equation from twice the second equation; you should be able to deduce the value of P knowing that it is an integer from the set {1, 2, ... , 9} and the fact that if something divides one side of an equation it divides the other. This makes it not too hard to then find M & S.

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