Solve the problem by writing an inequality.
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.
Let's assume the number of T-shirts the club needs to make and sell is represented by the variable "x".
The total cost to make x T-shirts can be expressed as:
Total Cost = $20 + $9 * x
The revenue generated from selling x T-shirts can be expressed as:
Total Revenue = $15 * x
To find the profit, we subtract the total cost from the total revenue:
Profit = Total Revenue - Total Cost = $15 * x - ($20 + $9 * x)
We want the profit to be at least $150, so we can write the inequality:
$15 * x - ($20 + $9 * x) ≥ $150
Simplifying the inequality:
$15x - $20 - $9x ≥ $150
$6x - $20 ≥ $150
$6x ≥ $170
x ≥ $170 / $6
x ≥ 28.33
Since we cannot make a fraction of a T-shirt, we round up to the next whole number.
Therefore, the club needs to make and sell at least 29 T-shirts to profit at least $150.