Question

The Art department at a high school is selling a collection book of sketches created by the

senior class for $9. It costs $250 to use the printer plus $3.00 per book. If they print 500
books, what is the least number of books they need to sell to make more than $1500?

Answer 1

167 books are needed to get above the minimum of 1500 dollars

Answer 2

362

Explanation:

The total of costs for printing 500 books is ...

$250 +500($3) = $1750

The profit is the difference between revenue and cost.

revenue -cost = profit

9b -1750 > 1500

9b > 3250

b > 3250/9 =361 1/9

The number of books they need to sell is at least 362.

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Additional comment

If the books could be printed one at a time, then the 9-3 = $6 contribution margin of each book would require sale of 250/6 = 41 2/3 books to cover the printer setup charge and 1500/6 = 250 books to achieve the desired profit, for a total of 292 books. However, the books were printed in a batch of 500, so the cost of printing those extra books must also be covered. That is why we need to sell 362 books for a profit of at least $1500.