Question

I really need help with this last problem

The students in the freshman class plan to use the profits from selling hats for a class trip. The cost to have 200 hats made is $1500. They will be sold for $12 each.



a. Write an equation to represent the profit, p, earned from selling x hats.



b. Use the equation you wrote in part a to find the minimum number of hats that must be sold for the class to recover the cost of making the 200 hats. Show your work or explain how you found your answer.



c. Suppose the class decides to charge $15 per hat instead of $12. At this selling price, how many fewer hats must be sold to recover the cost of making the 200 hats? Show your work or explain how you found your answer.

Answer 1

a. p=12*x

b. x=13

c. x=10, 3 fewer

Explanation:

a. hat is 12 ea. so profit, p, from selling x hats = 12*x

b. cost=1500

profit > cost to recover

12*x >= 1500

x >= 12.5 but no. of hats sold is integer

x=13

c. new price=15

15*x >= 1500

x >=10

x=10, 3 fewer hats

Answer 2

Explanation:

a. Profit, p, earned from selling x hats when hat will be sold for $12 each:

p = 12x

b. To recover the cost of making the 200 hats which is $1500, profit, p >= cost:

p = 12x >= 1500

x >= 1500/12 = 12.5

So the minimum number of hats that must be sold = 13

c. New hat price = $15 so p = 15x

p = 15x >= 1500

x >= 1500/15 = 10

So the new minimum = 10 which is 3 fewer.