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

May 25, 2018

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 $y$.

$2 x = 60$

Now solve for $x$ $\implies x = 30$

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

$y + 30 = 50$
$\implies y = 20$

The two numbers are $30$ and $20$

May 25, 2018

$30 \text{ and } 20$

#### Explanation:

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

$x + y = 50 \leftarrow \textcolor{b l u e}{\text{sum of numbers}}$

$x - y = 10 \leftarrow \textcolor{b l u e}{\text{difference of numbers}}$

$\text{add the 2 equations term by term on both sides}$

$\left(x + x\right) + \left(y - y\right) = \left(50 + 10\right)$

$2 x = 60$

$\text{divide both sides by 2}$

$x = \frac{60}{2} = 30 \Rightarrow x = 30$

$\text{substitute " x=30" into } x + y = 50$

$30 + y = 50$

$\text{subtract 30 from both sides}$

$y = 50 - 30 = 20 \Rightarrow y = 20$

$\text{the 2 numbers are 30 and 20}$

May 25, 2018

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:

$x + y = 50$

$\left(10 + y\right) + y = 50$

$10 + 2 y = 50$

$2 y = 40$

$y = 20$

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

$x - y = 10$

$30 - 20 = 10$