Respuesta :
The weight of John is 160 pounds and weight of Sally is 100 pounds.
Explanation
Suppose, the weight of John is [tex]x[/tex] pounds and the weight of Sally is [tex]y[/tex] pound.
Given that, the sum of their weight is 20 pounds more than four times the difference between their weights. So, the first equation will be....
[tex]x+y=4(x-y)+20 ...................................(1)[/tex]
Also given that, twice sally's weight is 40 pounds more than john's weight. So, the second equation will be.....
[tex]2y=x+40...............................(2)[/tex]
Simplifying equation (1) we will get....
[tex]x+y=4x-4y+20\\ \\ 3x-5y=-20 ...................................(3)[/tex]
Solving equation (2) for [tex]x[/tex] itself......
[tex]x= 2y-40[/tex]
Now substituting this [tex]x= 2y-40[/tex] into equation (3) in place of [tex]x[/tex], we will get.....
[tex]3(2y-40)-5y=-20\\ \\ 6y-120-5y=-20\\ \\ y=-20+120\\ \\ y=100[/tex]
Plugging [tex]y=100[/tex] into [tex]x= 2y-40[/tex] .....
[tex]x=2(100)-40=200-40=160[/tex]
So, the weight of John is 160 pounds and weight of Sally is 100 pounds.
