Math CentralQuandaries & Queries


Question from Rita, a student:

A store advertises that during its Labor Day sale $15 will be deducted from every purchase over $100. In addition, after the deduction is taken, the store offers an early-bird discount of 20% to any person who makes a purchase before 10 a.m. If Hakeem makes a purchase of x dollars, x > 100, at 8 a.m., what, in terms of x, is the cost of Hakeem's purchase?

(1) 0.20x - 15 (3) 0.85x - 20
(2) 0.20x - 3 (4) 0.80x - 12 ... This is the answer.

My work:

I understand the situation in the question. The correct answer is highlighted in red. I selected choice (1) given the fact that Hakeem purchased an item over $100 and that the store offers a discount of $15 and an additional discount of 20%.

It made sense to easily come up with 0.20x - 15. In fact, I also decided to let C = cost and then went on to develop the equation C = 0.20x - 15.

Why is choice (4) correct and my answer incorrect?

Hi Rita,

There are two errors in choice (1). First of all the discount is 20% so 0.20x dollars would be the amount of the discount not Hakeem's cost. Hakeem's cost is x - 0.20x = 0.80x dollars. Thus a possible answer might be 0.80x - 15 dollars but even that is incorrect. 0.80x - 15 dollars would be the cost if Hakeem got a 20% discount and then a further reduction of $15, but that's not what happened. First the $15 deduction is taken off so the price is reduced to x - 15 dollars. Then, since he is an early-bird shopper this price is reduced by 20%. Thus what he pays is 0.80 × (x - 15) = 0.80x - 12 dollars.

I hope this helps,

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS