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.