Question

Carol crocheted 150 caps to sell at the community center's fall festival. Carol spent $287 on yarn for the caps and she must pay

$75 for a booth space at the fall festival. If Carol sells the caps for $12 each, how many caps must she sell to make a profit and
what is the maximum profit that Carol can make?

Answer 1

To make a profit, Carol's revenue must be greater than her total costs. Her revenue is the number of caps she sells multiplied by the price per cap, or:

revenue = 12x, where x is the number of caps she sells.

Her total costs are the cost of yarn plus the cost of the booth space, or:

costs = 287 + 75 = 362.

To break even, her revenue must be equal to her costs, or:

12x = 362

Solving for x, we get:

x = 30.17

Since Carol cannot sell a fractional number of caps, she must sell at least 31 caps to break even.

To calculate the maximum profit, we need to find the revenue generated by selling all 150 caps, subtract the total costs, and then round down to the nearest dollar. The revenue generated by selling all 150 caps is:

revenue = 12 * 150 = 1800

The total costs are:

costs = 287 + 75 = 362

The profit is:

profit = revenue - costs = 1800 - 362 = 1438

Therefore, the maximum profit that Carol can make is $1,438, but she must sell at least 31 caps to break even.