Question

Luca sells hand -crafted puzzles for $22 each. The start -up cost for her business was $420 and each puzzle costs $13 to make. How many must she sell before making a profit?

Answer 1

To determine the number of puzzles Luca must sell before making a profit, calculate her total costs and revenue. Using the equation 22x - (420 + 13x) > 0, find x > 46.67. Therefore, Luca must sell at least 47 puzzles before making a profit.

Step-by-step explanation:

To determine the number of puzzles Luca must sell before making a profit, we need to calculate her total costs and total revenue.

1. First, let's calculate the total cost. The start-up cost is $420, and each puzzle costs $13 to make. If Luca sells x puzzles, her total cost would be: $420 + 13x.
2. Next, let's calculate the total revenue. Luca sells each puzzle for $22, so if she sells x puzzles, her total revenue would be: 22x.
3. To determine the point at which Luca makes a profit, we need to find the value of x that satisfies the equation: total revenue - total cost > 0. In other words, 22x - (420 + 13x) > 0.
4. Simplifying the equation, we get: 9x - 420 > 0.
5. Solving for x, we find: x > 46.67.

Therefore, Luca must sell at least before making a profit.