What is the least number of quilts the guild must sell for its profit to be more than $1,000?

Question

A quilting guild sells handmade quilts for $80 each at a craft fair. The guild paid $120 for booth space. The guild's profit is the money collected from quilt sales minus the $120 booth cost. The guild wants its profit to be more than $1,000.

Accepted Answer

15. If n is the number of quilts sold, the profit is 80n − 120, so 80n − 120 > 1000. Adding 120 gives 80n > 1120, and dividing by 80 gives n > 14. Because the profit must be more than $1,000, n = 14 gives a profit of exactly 80(14) − 120 = $1,000, which is not more than $1,000. The least whole number greater than 14 is 15. (Treating the inequality as 'at least $1,000' would incorrectly give 14, and forgetting the $120 booth cost would incorrectly give 1000 ÷ 80 = 12.5, or 13.)

Algebra practice question

Answer: 15

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