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.

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.

Answer 1

2-0.17=1.83

S/he makes 1.83 for each cupcake now we divide the cost

75/1.83=40.98

You cannot make 0.02 of a cupcake so you round up

41 cupcakes

75< X x 1.83

Explanation:

Answer 2

41 cupcakes

Explanation:

Let x be the number of cupcakes sold at the breakeven point where cost equals revenue realized.

-The cost and revenue functions are expressed as:

`Cost=75+0.17x\\\\\\Revenue=2x`

#Equate the two functions at breakeven:

`75+0.17x=2x\\\\75=7.83x\\\\x=40.98361\approx41 \ cupcakes`

Break-even is reached after the sale of 40.098361 cupcakes.

`Profit=Revenue -Cost\\\\=2x-(75+0.17x), \ \ x=41\\\\=2* 41-75-0.17* 41\\\\=0.03`

Hence, the first profits($0.03)are realized after the sale of 41 cupcakes.