Question

What are the two numbers that are the sum 50 difference 10 ? thank you

Answer 1

See below.

Explanation:

Firstly, assign the two numbers random variables `x` and `y`

The sum of them is equal to `50` therefore

`x+y=50`

The difference is `10`

`x-y=10`

Now we have a simultaneous equation.
`x+y=50`
`x-y=10`

Add them together to cancel out the `y`.

`2x=60`

Now solve for `x` `=> x=30`

Now put the value back into one of the equations to find `y`

`y+30=50`
`=> y=20`

The two numbers are `30` and `20`

Answer 2

`30" and "20`

Explanation:

`"let the 2 numbers be x and y ";x>y`

`x+y=50larrcolor(blue)"sum of numbers"`

`x-y=10larrcolor(blue)"difference of numbers"`

`"add the 2 equations term by term on both sides"`

`(x+x)+(y-y)=(50+10)`

`2x=60`

`"divide both sides by 2"`

`x=60/2=30rArrx=30`

`"substitute " x=30" into "x+y=50`

`30+y=50`

`"subtract 30 from both sides"`

`y=50-30=20rArry=20`

`"the 2 numbers are 30 and 20"`

Answer 3

30 and 20

Explanation:

Okay let's define a couple numbers, let's call one of them `x` and the other `y`.

We are told that the sum (addition) is:

`x+y =50`

And the difference (subtraction):

`x-y=10`

We have a system of equations; two equations and two unknown variables so it is solvable; we will use the "substitution" method:

add `y` to both sides of: `x-y=10`

`x-y +y=10+y`

`x=10+y`

now substitute the value we solved for `x` into the other equation:

`x+y =50`

`(10+y)+y =50`

`10+2y =50`

`2y =40`

`y=20`

So one of the numbers is `20`. to find the other use either of our original equations and insert `y` to solve for `x`, this one is simplest:

`x+y =50`

`x+20 =50`

`x =30`

Solved! Our numbers are 30 and 20

To check your solutions insert them into the original equations:

`x+y =50`

`30+20 =50`

and

`x-y=10`

`30-20=10`