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

Jun 27, 2018

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 $- 3 x$, from the second, $y$, is $= 4$, so

$y - 3 x = 4$

Now you have a simultaneous equation to work with.

$y + x = 56$

$y - 3 x = 4$

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.

$3 \left(y + x\right) = 3 \left(56\right)$
$y - 3 x = 4$

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

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

$4 y = 172$

$y = \frac{172}{4}$

$y = 43$

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,

$\left\{\begin{matrix}x = 13 \\ y = 43\end{matrix}\right.$