Question

Question #bf493

Answer 1

`x=500`
`y=700`

Explanation:

One number is less than 3 times the other.

Let us say that the "One number" is `x`, and the other is `y`.
We get the following equations

`x=3y-800`
`x+y=1200`

Subtract `-3y` from the first equation.

`x-3y=-800`

Multiply the first equation by `-1`.

`-x+3y=800`

Now, add the two equations together.

`-x+3y=800`
`x+y=1200`

`4y=2000`

Divide both sides by `4`.

`y=500`

Substitute `y=500` into either of the 2 equations. This time, I'll use the second one simply because it's easier.

`x+500=1200`

`x=700`

Oh but wait, it says the smaller number is `x`!
No problem, just change the variables.

`x=500`
`y=700`

Check :

`500*3-800` does indeed equal `y`, which is `700`.
`800+700` does indeed equal `1200`.

Answer 2

The numbers are `500 and 700`

Explanation:

We can define both the numbers using one variable.

Let the one number be `color(blue)(x)`
.
The other is `800` less than `3` times `x`

The other number is therefore: `color(blue)(3x-800)`

Their sum is `1200`

`x + 3x -800 = 1200`

`4x = 1200+800`
`4x = 2000`

`x = 500 and 3x -800 = 700`

The numbers are `500 and 700`