Final answer:
To determine the number of cakes required to make a profit, an inequality is set up by comparing total revenues with total costs. With operating costs of $800 and a cost of $10 per cake, the inequality is 15c > 800 + 10c. Solving this, the bakery must sell more than 160 cakes daily to make money.
Step-by-step explanation:
The student's question regards determining the number of cakes a bakery must sell each day to make money, given a daily operating cost and the cost per cake. To calculate this, we need to set up an inequality that compares the bakery's costs with its revenues. The fixed operating costs are $800 per day, and each cake costs $10 to make. Each cake sells for $15. If c represents the number of cakes sold, then the cost of making c cakes is $10c and the revenue from selling c cakes is $15c. The bakery makes money on any given day when the revenue exceeds the total costs (fixed operating costs plus the cost of making the cakes). The inequality to represent this situation is Solving the inequality gives us the minimum number of cakes that need to be sold to make a profit:
15c - 10c > 800
5c > 800
c > 160
Therefore, the bakery must sell more than 160 cakes a day to make money.