Question

Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 each as a fund-raiser. It costs $20, plus $6 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.

Answer 1

Let is us suppose club needs to make x T-shirts in order to profit at least $100.

Then the selling price is given by

$\text{Selling Price }= 12x$

Now, we have been given that it costs $20, plus $6 per T-shirt to make the T-shirts. Thus, the cost price is given by

$\text{Cost Price }= 20+6x$

Now, profit is given by

Profit = Selling price - cost price

$= 12x-20-6x\\ \\ =6x-20$

Now, we have been given that profit is at least $100. Therefore, we have the inequality

$6x-20\geq 100$

Add 20 to both sides

$6x\geq 120\\ \\ x\geq 20$

Thus, the club needs to sell 20 T-shirts in order to make at least profit of $100