# The sum of two numbers is 12 Their difference is 4. How do you find the numbers?

Mar 19, 2017

$8 \text{ and } 4$

#### Explanation:

Let the 2 numbers be x and y with x > y

$\Rightarrow x \textcolor{red}{+ y} = 12 \to \left(1\right) \leftarrow \text{sum of 2 numbers}$

$\Rightarrow x \textcolor{red}{- y} = 4 \to \left(2\right) \leftarrow \text{ difference of numbers}$

Adding the 2 equations, term by term on both sides, will eliminate y leaving an equation in x that we can solve.

$\Rightarrow \left(1\right) + \left(2\right) \text{ gives}$

$\left(x + x\right) + \left(\textcolor{red}{- y + y}\right) = \left(4 + 12\right)$

$\Rightarrow 2 x = 16$

divide both sides by 2

$\frac{\cancel{2} x}{\cancel{2}} = \frac{16}{2}$

$\Rightarrow x = 8$

Substitute this value into equation ( 1 ) and solve for y

$\Rightarrow 8 + y = 12$

$\Rightarrow y = 12 - 8 = 4$

$\text{Thus the 2 numbers are " 8" and } 4$

Mar 19, 2017

$a = 4$
$b = 8$

#### Explanation:

let these two numbers be $a$ and $b$.

$a + b = 12$
$a - b = 4$

if you add the two equations:

$a + b = 12$
$a - b = 4$

$2 a + 0 = 8$
$2 a = 8$

divide by $2$:
$a = 4$

substitute:
$a + b = 12$
$4 + b = 12$
$b = 12 - 4$
$= 8$

$a = 4$
$b = 8$

$8 + 4 = 12$
$8 - 4 = 4$

Mar 19, 2017

There are two numbers so you need two equations. Solve for one variable ( number) and then substitute and solve for the other.

$x = 8 \mathmr{and} y = 4$

#### Explanation:

Let $x$ equal one number and $y$ the other number.

One equation would be the sum of the numbers.

$x + y = 12$

the other equation would be the difference of the two numbers

$x - y = 4 \text{ }$

$x + y = 12 \text{ " and " "x -y = 4" }$(adding $+ y \mathmr{and} - y = 0$)

so $2 x = 16 \text{ }$ Now divide both sides by 2

$\frac{2 x}{2} = \frac{16}{2} \text{ }$ This gives

$x = 8$ Now substitute x into one of the equations and solve for y

$8 + y = 12 \text{ }$ subtract 8 from both sides

$8 - 8 + y = 12 - 8 \text{ }$ This gives

$y = 4 \text{ }$ Put values into the second equation to check

$8 - 4 = 4$

$4 = 4 \text{ }$ check

$x = 8 \mathmr{and} y = 4$

Mar 22, 2017

The numbers are $4 \mathmr{and} 8$

#### Explanation:

Questions which involve two or more numbers can be done using one variable to define them all.

Let the smaller number be $\textcolor{red}{x}$.

The difference between the numbers is $4$.

The other number is $\textcolor{b l u e}{x + 4}$

Their sum is $12$

$\textcolor{red}{x} + \textcolor{b l u e}{x + 4} = 12$

$2 x = 12 - 4$

$2 x = 8$

$x = 4$

$\therefore x + 4 = 8$

The numbers are $4 \mathmr{and} 8$