3
algebra

A bakery sells cakes for $25 each. The ingredients cost $8 per cake, and the monthly rent is $600. How many cakes cc must be sold to make a profit of at least $1000 this month?

A

c95c \geq 95

B

c64c \geq 64

C

c32c \geq 32

D

25c8c600100025c - 8c - 600 \geq 1000

Correct Answer: A

Choice A is the correct answer. Profit is calculated as Revenue minus Costs.

  1. Revenue: $25 per cake (25c25c)
  2. Variable Cost: $8 per cake (8c8c)
  3. Fixed Cost: $600 rent
  4. Profit Equation: Profit = Revenue - Variable Cost - Fixed Cost
  5. Inequality: (25c8c)6001000(25c - 8c) - 600 \geq 1000
  6. Simplify: 17c600100017c - 600 \geq 1000
  7. Add 600: 17c160017c \geq 1600
  8. Divide by 17: c94.11...c \geq 94.11...
  9. Round up: Since you can't sell a fraction of a cake, c95c \geq 95

?�� Strategic Tip: Net profit per unit is (Selling Price - Cost per unit). Total Profit = (Net per unit × Quantity) - Fixed Costs.

Choice B is incorrect because it ignores the variable cost of ingredients (25c600100025c - 600 \geq 1000). Choice C is incorrect because it ignores the rent (17c100017c \geq 1000). Choice D is incorrect because while the setup is correct, Choice A is the solved answer, and D is just the setup (though mathematically valid, A is the explicit solution requested by "How many cakes..."). Wait, usually solving is preferred. Let's re-read. "How many cakes..." implies finding the value. A is the best answer. D is the setup.

Correction: Choice D is the setup, but A is the solution. The question asks "How many cakes", so A is the answer.