Alex stocks up for winter. he buys 24 cans of vegetables. he pays 80 cents per can for tomatoes and 40 cents per can for corn, for a total cost of $12.8. how many cans of corn does he buy?

Let x be the number of cans of corn Alex buys. Let y be the number of cans of tomatoes Alex buys. Establish the equations: Equation 1: x+y=24 Equation 2: 0.40x+0.80y=12.8 Isolate y in equation 1: y = 24-x Substitute y= 24-x into equation 2: 0.40x+0.80(24-x)=12.8 0.40x+19.2-0.80x=12.8 -0.40x = -6.4 x=16 Therefore, Alex buys 16 cans of corn.