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

To solve for the weights of John and Sally, we need to set up and solve two linear equations based on the given information. Simplifying the first equation and solving the system of equations will give us the weights of John and Sally.

Step-by-step explanation:

Let's define the weights of John and Sally as J and S, respectively.

According to the first fact, the sum of John's weight and Sally's weight is 20 pounds more than four times the difference between their weights:

J + S = 4(J - S) + 20

According to the second fact, twice Sally's weight is 40 pounds more than John's weight:

2S = J + 40

To simplify the first equation, we can distribute the 4 on the right side:

J + S = 4J - 4S + 20

Combining like terms, we get:

3J - 5S = 20

Now, we have two linear equations:

2S = J + 40

3J - 5S = 20

Let's solve these equations to find the weights of John and Sally.

Answer 2

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.