Question

The sum of two numbers is 30 and their difference is 20. What are the two numbers?

Answer 1

5 and 25

Explanation:

`x+x-20=30`
`2x-20 =30`
`2x -20 +20 = 30+20`
`2x = 50`

`x= **25**`

`x-20 = **5**`

Answer 2

`(x,y)=(25,5)`

Explanation:

Two numbers, x and y, have this relationship:

`x+y=30`

`x-y=20`

We can solve this - it's 2 equations with 2 unknowns. I'll take the second equation, solve for x, then substitute into the first one:

`x-y=20`

`x=20+y`

And so

`x+y=30`

`(20+y)+y=30`

`20+2y=30`

`2y=10`

`y=5`

We can now substitute this back into either starting equation - I'll do both to show that it works in both:

`x+y=30`

`x+5=30`

`x=25`

`x-y=20`

`x-3=20`

`x=25`

It all checks!

`(x,y)=(25,5)`

Answer 3

one number is `25` the other number is `5`

Explanation:

The problem asks for the identity of two unknown numbers.
This makes the problem one with two variables.
With two variables it is necessary to have two equations.

Let x be one number
Let y be the other number.

`x + y = 30` ( the sum of the two numbers is 30 )
`x -y = 20` ( The difference of the two numbers is 20)

Solving the second equation for x

`x - y + y = 20 +y` This gives

`x = 20 + y`

Substituting this value into the first equation gives.

`20 + y + y = 30` combining like terms and subtracting 20 gives

`20 - 20 + 2y = 30 - 20` This gives

 #2y  =   10#    Dividing both sides by #2# to isolate #y# results in

`(2y)/2 = 10/2` solving this gives

`y= 5" "` Put the value of 5 for y into either equation to find x

`x + 5 = 30" "` subtract 5 from both sides.

`x + 5 -5 = 30 -5` resulting in

`x = 25`

The two unknown numbers are `5 and 25`