Question

Two numbers sum to 56. thrice the first subtracted from the second is 4. find the numbers?

Answer 1

The two numbers are `13` and `43`.

Explanation:

There are two numbers. Let's call them `x` and `y`.

`x + y = 56`

Thrice the first subtracted, so `-3x`, from the second, `y`, is `= 4`, so

`y - 3x = 4`

Now you have a simultaneous equation to work with.

`y + x = 56`

`y - 3x = 4`

Same signs subtract, Different signs add. I always prefer dealing with the number after the operation, so I'll start with that. We should make the coefficients the same.

`3(y+x) = 3(56)`
`y - 3x = 4`

`3y + 3x = 168`
`y - 3x = 4`

If we add the bottom to the top, we end up with

`4y = 172`

`y = 172/4`

`y = 43`

Substitute your answer for `y` into any of the equations given (and never the one that you made, in case it is wrong).

Let's take the given one.

`x + y = 56`

`x + 43 = 56`

`x = 56-43`

`x = 13`

Therefore,

`{(x = 13), (y = 43) :}`