Question

3. Keji makes cakes to sell at the farmer's market. It costs $135 to rent tableat the market. The cost of baking supplies to make a cake is $4.50. Keji sellscakes for $12 each. The inequality 12n > 135 +4.50n represents the situation inwhich Keji makes a profit.3a. Will Keji make a profit if she sells 15 cakes? Show or explain how youknow.2 points3b. Write an inequality to show the number of cakes, n, Keji must sell tomake a profit.3c. Explain how you arrived at your answer for question (3b)

Answer 1

Price of the rent table: $135

Price of baking supplies: $4.50

Price of one cake: $12

Profit inequality: 12*n > 135 + 4.50*n ...(1)

Where n is the number of cakes Keji sells

3a.

For n = 15

Replacing in (1):

12*15 > 135 + 4.50*15

180 > 202.50

But this inequality is false, so we conclude that Keji will not make a profit if he sells only 15 cakes.

3b.

From (1), we solve the inequality for n:

12*n - 4.50*n > 135

7.5*n > 135

n > 18 ...(2)

From the inequality (2), we conclude that Keji needs to sell at least 18 cakes to make a profit.

3c.

This is explained above