Bunyan Farm sells 3 pound and 5 pound bags of onions. The Tuesday morning delivery consists of 34 bags weighing 122 pounds. How many bags are there of each size?

24 3-pound bags (72 pounds) and 10 5-pound bags (50 pounds). 72+50 = 122 pounds, 24+10 bags = 34 bags

24 - 3 pound bags and 10-5 pound bags

I set up a system of equations

3x + 5y = 122

x + y = 34

Multiply the second equation by - 3 so that the x's cancel. This gets you y = 10. Plug 10 back in to either original equation and x = 24.