Three bags of wheat, two bags of corn, and one bag of oats weigh the same as one bag of wheat, one bag of corn and five bags of oats. If two bags of corn and one bag of oats weighs 26 pounds, and one bag of corn weighs 10 pounds, how much does one bag of wheat weigh?

X = wheat, y = corn, z = oats

3x + 2y + z = x + 5z

2y + z = 26

y = 10 ... corn weighs 10 lbs

2y + z = 26

2 (10) + z = 26

20 + z = 26

z = 26 - 20

z = 6 ... oats weigh 6 lbs

3x + 2y + z = x + 5z

3x + 2 (10) + 6 = x + 5 (6)

3x + 26 = x + 30

3x - x = 30 - 26

2x = 4

x = 4/2

x = 2 < = = = wheat weighs 2 lbs

A bag of wheat equals 7 pounds