# Question 41282

Jan 8, 2018

11 and 16

#### Explanation:

First, write the problem in the form of a system of equations:
$27 = x + y$
$x = 2 y - 6$

Next, using substitution, combine the two equations replacing x in the first equation with the value of x in the second:
$27 = \left(2 y - 6\right) + y$

Then, simplify and solve for y:
$27 = 3 y - 6$
$33 = 3 y$
$y = 11$

Finally, plug in the value of y into the original equation and solve for x:
$27 = x + 11$
$x = 16$

You can check your values of x and y by plugging them into both original equations and determining if they fulfill it:
$27 = 11 + 16$
$27 = 27$ Check

$16 = 2 \left(11\right) - 6$
$16 = 22 - 6$
$16 = 16$ Check

Jan 8, 2018

$11 \text{ and } 16$

#### Explanation:

$\text{let the 2 numbers be "x" and } y$

"then "x+y=27color(white)(x);x>y#

$\text{larger number } x = 2 y - 6$

$\Rightarrow 2 y - 6 + y = 27$

$\Rightarrow 3 y - 6 = 27$

$\text{add 6 to both sides}$

$\Rightarrow 3 y = 33 \Rightarrow y = 11$

$\text{substitute into } x + y = 27$

$\Rightarrow x + 11 = 27 \Rightarrow x = 16$

Jan 8, 2018

$\text{The numbers are } 11 \mathmr{and} 16$

#### Explanation:

To solve it, assumed the following variables:
Let x= the smaller number
Let y= the bigger number

Now, formulate equations that relate the assumed numbers as prescribed in the problem; hence,

$x + y = 27 \to e q .1$
$y = 2 x - 6 \to e q .2$

Then, solve the problem through substitution method; given the value of $y$ as shown in the formulated $e q .2$ above. So that:

$x + \textcolor{red}{y} = 27$, substitute the value of y

$x + \textcolor{red}{\left(2 x - 6\right)} = 27$, simplify the equation

$x + \textcolor{red}{2 x - 6} = 27$, combine like terms

$3 x - 6 = 27$, add $6$ both sides of the equation to isolate the term with variable $x$.

$3 x - 6 + 6 = 27 + 6$, simplify and combine like terms

$3 x = 33$, divide both sides by $3$

$x = 11$

$\text{Therefore:}$

$\textcolor{red}{x = 11}$

$y = 2 x - 6 \to e q .2$, substitute the value of $x = 11$

$y = 2 \left(11\right) - 6$

$y = 22 - 6$

$\textcolor{b l u e}{y} = 16$

Check:
$\textcolor{red}{x} + \textcolor{b l u e}{y} = 27$
$11 + 16 = 27$
$27 = 27$