The sum of two numbers is 4. Twice the larger is 11 more than the smaller. How do you find the smaller number?

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Answer 1 · 2017-01-05T08:58:19

The smaller number is $-1$ .

Considering the two numbers as $x$ and $y$ where $x$ is the larger number, we can write:

$x+y=4$
$2x=y+11$

From the first equation, we can determine a value for $x$ .

$x+y=4$

Subtract $y$ from both sides.

$x=4-y$

In the second equation, substitute $x$ with $color(red)((4-y))$ .

$2x=y+11$

$2color(red)((4-y))=y+11$

Open the brackets and simplify. The product of a positive and a negative is a negative.

$8-2y=y+11$

Add $2y$ to both sides.

$8=3y+11$

Subtract $11$ from both sides.

$-3=3y$

Divide both sides by $3$ .

$-1=y$ or $y=-1$

In the first equation, substitute $y$ with $color(blue)(-1)$ .

$x+y=4$

$x+(color(blue)(-1))=4$

Open the brackets and simplify. The product of a positive and a negative is a negative.

$x-1=4$

Add $1$ to both sides.

$x=5$