How do I solve this inequality word problem?

Question

I need to solve this but I don't know how to set up the 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."

Answer 1

Where n is the number of T shirts:

Cost = 20+8n

Income = 12n

Profit = Income - cost

Income - cost > 100

12n - (20 + 8n) >100

12n - 20 - 8n >100

4n > 120

n>30

So at least 30 T shirts must be sold.

Answer 2

Ok. if you want it in inequality format, here ya go:

Look at the facts:

1 T-shirt = $12 --> you are profiting from this so its +

it costs $8 to make 1 shirt + $20 ---> you are losing this so its -

SO: if you want to make at least $100 dollars, that means it can be $100 or more

so lets make x= the # of shirts

$12(x) - ($20+ $8(x)) ≥ $100

$4x- $20 ≥ $100

$4x ≥ 120

x ≥ 30 shirts

So you need to make AT LEAST 30 SHIRTS