Question

The sum of john's weight and sally's weight is 20 pounds more than four times the difference between their two weights (john is heavier). Twice sally's weight is 40 pounds more than john's weight. Write down the two facts in two linear equations. Simplify the first equation and solve the two equations to find weights of john and sally

Answer 1

The weight of John is 160 pounds and weight of Sally is 100 pounds.

Explanation

Suppose, the weight of John is $x$ pounds and the weight of Sally is $y$ 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....

$x+y=4(x-y)+20 ...................................(1)$

Also given that, twice sally's weight is 40 pounds more than john's weight. So, the second equation will be.....

$2y=x+40...............................(2)$

Simplifying equation (1) we will get....

$x+y=4x-4y+20\\ \\ 3x-5y=-20 ...................................(3)$

Solving equation (2) for $x$ itself......

$x= 2y-40$

Now substituting this $x= 2y-40$ into equation (3) in place of $x$, we will get.....

$3(2y-40)-5y=-20\\ \\ 6y-120-5y=-20\\ \\ y=-20+120\\ \\ y=100$

Plugging $y=100$ into $x= 2y-40$ .....

$x=2(100)-40=200-40=160$

So, the weight of John is 160 pounds and weight of Sally is 100 pounds.