Question

Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.

Answer 1

An algebraic equation containing an inequality may contain symbols such as <, >, ≤ and ≥. You should know the concept of profit first. Profit is the net income you acquired by getting the total revenue, and subtracting from it all the fixed and variable costs. So, in equation, that would be

Profit = Revenue - (Fixed Cost + Variable Cost)

You should note that the limit for profit is at least $100. So that means it can be more than $100 but can't be less than. Therefore, the symbol to be used is greater than or equal to, symbolized by ≥. Then the equation is

12x - (20 + 8x) ≥ 100, where x represents the minimum number of t-shirts to reach a profit of at least $100. Solving the equation,

12x - 20 - 8x ≥ 100
12x - 8x ≥ 100 + 20
4x ≥ 120
x ≥30

Therefore, the club needs to sell at least 30 shirts.