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