The School Fundraiser

Pre-Algebra · Axiom Academy

Your class runs a popcorn booth. Three equations tell you whether you make money — and exactly how many bags you must sell to hit your goal. First, the money coming in . If each bag sells for p and you sell n bags, your revenue is just price times quantity. There is nothing fancy here: sell more bags, or charge more per bag, and the rectangle of revenue grows. We will set the price at 5 a bag, a normal carnival price. Revenue is one side times the other Each new bag adds a column of height 5 , so the revenue rectangle widens one bag at a time. At n = 120 bags and 5 each, revenue is dollars. That is money taken in — not yet profit, because we have not paid for anything. Now the money going out . Cost has two parts: a fixed 80 (booth + popper) that you owe even if you sell nothing, plus 2 for every bag. Profit is what is left after you subtract cost from revenue. Watch the revenue bar and the cost bar both climb as bags sell — the gap between them is the profit. 80 + 2n — starts at 80 , grows 2 per bag. Where the bars meet: profit = 0 . At the start, cost is ahead — you have paid 80 and sold nothing, so profit is negative. Each bag earns 5 but costs 2 , so it adds 3 of profit. Break-even is where revenue first catches cost: solving 5n = 80 + 2n gives 3n = 80 , so . You first turn a profit at 27 bags ; every bag after that is gravy. 3. How Many Bags to Hit the Goal?

This is the written version of the interactive lesson above. See the full Pre-Algebra course.