Question

The student council is selling cupcakes at the school play. ​The cost to ​make the cupcakes is a fixed $75 plus $0.17 per cupcake made. ​ ​Each ​cupcake sells for $2.00. ​ ​Part A Write an equation for the cost, C, of making x cupcakes and ​an equation for the revenue, R, from selling x cupcakes. ​ ​ C= ​ R= ​Part B Write an inequality that could be solved to find the number of ​cupcakes, x, that the student council must make and sell to ​make ​a profit. ​ ​ ​​Part C Solve the inequality, and determine how many cupcakes must ​be sold to make a profit. ​ x≥ cupcakes.

Answer 1

Answer:

C = 75 + 0.17x and R = 2x

2x - (75 + 0.17x) > 0

x ≥ 41

Step-by-step explanation:

The cost to make the cupcakes is a fixed $75 plus $0.17 per cupcakes made and the selling price of each cupcake is $2.00.

Part A: Now, the equation for the cost, C, for making x cupcakes is  

C = 75 + 0.17x ......... (1)

Again the equation for the revenue, R, from selling x cupcakes is

R = 2x ............ (2)

Part B: So, the inequality that could be solved to find the number of cupcakes, x, that must be made and sold to make a profit is  

R - C > 0

2x - (75 + 0.17x) > 0 ......... (3)

Part C: Solving inequality (3) we get

(2 - 0.17)x > 75

⇒ x > 40.98

⇒ x ≥ 41 {Since, x can not be a fraction}

(Answer)