A club decides to sell T-shirts for $15 as a fundraiser. It costs $20 plus $9 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 $150.

Question

GPT 3.5 · Answer

Let $ x $ represent the number of T-shirts the club needs to make and sell. The revenue from selling the T-shirts would be the price per T-shirt (\$15) multiplied by the number of T-shirts ($x$): Revenue = $15$x$ The cost of making the T-shirts includes a fixed cost of $20 plus $9 per T-shirt. So, the total cost can be expressed as: Cost = $20 + $9$x$ To make a profit at least $150, the revenue needs to be at least $150 more than the cost. Therefore, the equation to solve is: \$15$x$ $\geq$ \$20 + $9$x$ + $150 Simplifying the equation: $15$x$ - $9$x$ $\geq$ $170 $6$x$ $\geq$ $170 Next, divide both sides of the equation by $6 to solve for $x$: $x$ $\geq$ $170 / $6 $x$ $\geq$ 28.33 Since the number of T-shirts must be a whole number, the club needs to make and sell at least 29 T-shirts in order to profit at least $150.