The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. How do you find the numbers?

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The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. How do you find the numbers?

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Answer 1 · 2015-09-25T14:49:40

$x = 13$ $x = 13$
$y = 31$ $y = 31$

Explanation:

You have two unknown numbers, we shall name them $x$ $x$ and $y$ $y$ .

Then we look at the information about these unknowns that is given, and write them out to get a picture of the situation.

The second number, which we have called $y$ $y$ , is 5 more than twice the first. To represent this, we write
$y = 2 x + 5$ $y = 2x + 5$
where $2 x$ $2x$ comes from 'twice the first', and
$+ 5$ $+5$ comes from '5 more'.

The next piece of information states that the sum of $x$ $x$ and $y$ $y$ is 44. We represent this as $x + y = 44$ $x+y = 44$ .

Now we have two equations to work off.

To find $x$ $x$ , substitute $y = 2 x + 5$ $y = 2x + 5$ into $x + y = 44$ $x+y = 44$ .
We then get
$x + (2 x + 5) = 44$ $x + (2x + 5) = 44$
$3 x + 5 = 44$ $3x + 5= 44$
$3 x = 44 - 5$ $3x = 44 - 5$
$3 x = 39$ $3x = 39$
$x = \frac{39}{3}$ $x = 39/3$
$x = 13$ $x = 13$

Now we know the value of $x$ $x$ , we can use it to find $y$ $y$ .
We take the 2nd equation, and plug in $x = 13$ $x=13$ .
$x + y = 44$ $x+y = 44$
$13 + y = 44$ $13+y = 44$
$y = 44 - 13$ $y = 44-13$
$y = 31$ $y = 31$

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The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. How do you find the numbers?

1 Answer

Explanation:

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