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.

The solution:

Let the minimum number of T-shirts that the club needs to make be x.

The the selling price of x t-shirts is $12x.

The cost price of x t-shirts is $20+$8x.

Profit should be $100

Therefore by the problem,

Cost price - selling price should be greater than equal to $100

therefore

12x - (20+8x) >=100; which is the required inequation

We now solve to find out the minimum number of t-shirts

12x - (20+8x) >=100

or, 12x-20-8x>=100

or, 4x>=100+20

or, 4x>=120

or, x>=30

Therefore the minimum number of t-shirts is 30.

you can check it by actual calculation.

100 divid by 12 and that is your answer which is about 9 t-shirts