Hi there! Can I get some help please?

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.

1 Answer
Sep 12, 2017

30

Explanation:

Cost (in $) as a function of the number of shirts made:

$$C(n)=20+8n$$

Money made (in $) as a function of the number of shirts sold:

$$M(n)=12n$$

Profit = money made - cost

$$P(n)=12n-(20+8n) = 4n-20$$

We want profit to be at least $100

$$P(n)\ge100$$
$$4n-20\ge100$$
$$4n\ge120$$
$$n\ge30$$

So they have to sell at least 30 shirts.