A printing plant that produces baseball cards has a monthly overhead of $6,000. It costs 18 cents to print each card, and the cards sell for 30 cents each. How many cards must the printing plant sell each month in order to make a profit?

A printing plant that produces baseball cards has a monthly overhead of $6,000. It costs 18 cents to print each card, and the cards sell for 30 cents each. How many cards must the printing plant sell each month in order to make a profit?

Detailed Explanation

Let x = the number of cards printed and sold each month.

Cost is equal to 6000 + 18x, and revenue is equal to 0.30x. You're looking for the point where revenue is greater than the cost (revenue > cost). The inequity is 0.30x > 6000 + 18x. Subtracting 18x from both sides of the inequity results in 0.12x > 6000.

Divide both sides by 0.12. The result is that x > 50,000. The printing plant would have to print and sell 50,000 cards per month to make a profit.

Cost is equal to 6000 + 18x, and revenue is equal to 0.30x. You're looking for the point where revenue is greater than the cost (revenue > cost). The inequity is 0.30x > 6000 + 18x. Subtracting 18x from both sides of the inequity results in 0.12x > 6000.

Divide both sides by 0.12. The result is that x > 50,000. The printing plant would have to print and sell 50,000 cards per month to make a profit.