Question #41282

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Question #41282

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Answer 1 · 2018-01-08T20:03:13

11 and 16

Explanation:

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

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

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

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

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

$16 = 2 (11) - 6$ $16 = 2(11) - 6$
$16 = 22 - 6$ $16 = 22 - 6$
$16 = 16$ $16 = 16$ Check

Answer 2 · 2018-01-08T20:05:37

$11 and 16$ $11" and "16$

Explanation:

$let the 2 numbers be x and y$ $"let the 2 numbers be "x" and "y$

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

$larger number x = 2 y - 6$ $"larger number "x=2y-6$

$\Rightarrow 2 y - 6 + y = 27$ $rArr2y-6+y=27$

$\Rightarrow 3 y - 6 = 27$ $rArr3y-6=27$

$add 6 to both sides$ $"add 6 to both sides"$

$\Rightarrow 3 y = 33 \Rightarrow y = 11$ $rArr3y=33rArry=11$

$substitute into x + y = 27$ $"substitute into "x+y=27$

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

Answer 3 · 2018-01-08T20:35:20

$The numbers are 11 and 16$ $"The numbers are " 11 and 16$

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,

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

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

$x + y = 27$ $x+color(red)(y)=27$ , substitute the value of y

$x + (2 x - 6) = 27$ $x+color(red)((2x-6))=27$ , simplify the equation

$x + 2 x - 6 = 27$ $x+color(red)(2x-6)=27$ , combine like terms

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

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

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

$x = 11$ $x=11$

$Therefore:$ $"Therefore:"$

$x = 11$ $color(red)(x=11)$

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

$y = 2 (11) - 6$ $y=2(11)-6$

$y = 22 - 6$ $y=22-6$

$y = 16$ $color(blue)y=16$

Check:
$x + y = 27$ $color(red)(x)+color(blue)y=27$
$11 + 16 = 27$ $11+16=27$
$27 = 27$ $27=27$

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Question #41282

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