Question

I don't know why this confused me so much but i cant figure it out no matter how much i read it can some one please help me xD

Arnold bought 19 gallons of milk in gallon and half-gallon jugs. If he bought a total of 24 jugs, how many of each size did he buy?

Answer 1

x = gallon jugs, y = 1/2 gallon jugs

x + y = 24 .....x = 24 - y
x + 1/2y = 19

24 - y + 1/2y = 19
-2/2y + 1/2y = 19 - 24
-1/2y = - 5
y = -5 / (-1/2)
y = -5 * -2
y = 10 <=== he bought 10 half gallon jugs

x + y = 24
x + 10 = 24
x = 24 - 10
x = 14 <=== he bought 14 gallon jugs