Question

Joanna uses the function p = (n) = 30n − 450 to calculate the profit, p, in dollars that she makes from selling n cakes in her store.

1. Write a formula for a function to calculate the number of cakes Joanna needs to sell for a given profit.
2. Calculate the minimum number of cakes that Joanna must sell to make a profit of at least $500.00.
Enter your answers in the spaces provided. Enter only your answers.


Formula: n = -1 (p) =

Minimum number of cakes:

Answer 1

a) n = (p + 450) / 30

b) The Minimum number of cakes is 32

Explanation:

Given that:

p = 30n - 450, where p is the profit in dollars from selling a number of cakes

(n).

a) to calculate the number of cakes (n) needed to be sold for a given profit, we need to make the number of cakes (n) the subject of formula for the equation.

p = 30n - 450

Adding 450 to both sides:

p + 450 = 30n - 450 + 450

30n = p + 450

Dividing through by 30:

30n / 30 = (p + 450) / 30

n = (p + 450) / 30

b)

If the profit is at least $500, the Minimum number of cakes (n) is:

n > (p + 450) / 30

n > (500 + 450) / 30

n > 950 / 30

n > 31.67

n ≈ 32

The Minimum number of cakes is 32