Question

Blake sells handcrafted pens to earn extra money. He knows he can sell the pens for $15 each. He will have to buy special machinery for $125 and supplies which cost $4.50 per pen. Write an inequality to represent the number of pens Blake must sell in order to make a profit.

Answer 1

The inequality to represent the number of pens Blake must sell to make a profit is $15x > $125 + $4.50x. This inequality factors in the fixed cost of machinery and variable supplies cost against the revenue from pen sales. Solving for x gives the minimum number of pens to sell for profit.

Step-by-step explanation:

To determine the number of pens Blake must sell to make a profit, we need to construct an inequality that compares his costs with his revenues. Blake's costs consist of a fixed cost for the machinery and a variable cost for the supplies needed for each pen. His revenue is the amount he earns from selling each pen.

Let's denote the number of pens Blake sells as x. The revenue earned from selling x pens is $15 multiplied by x, or $15x. The cost of the special machinery is a one-time cost of $125, plus the per-pen cost of supplies which is $4.50 per pen, amounting to $4.50x for x pens.

For Blake to make a profit, the revenue must be greater than the total cost. The inequality representing this condition is:

$15x > $125 + $4.50x

This inequality shows that the money made from selling pens has to be more than the total cost of machinery and supplies. To solve for x, Blake will need to sell enough pens so that the inequality holds true.