The difference between two numbers is 5. 6 less than twice the smaller number is the larger number. What are the numbers?

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Answer 1 · 2018-03-26T00:37:58

The two numbers are 16 and 11.

Let's call the two numbers $x$ and $y$ .

According to the question, the difference between the two numbers is 5, so:

$x-y=5$

In this case, the difference is a positive number, so that means $y$ is smaller than $x$ .

The next statement is "6 less than twice the smaller number is the larger number". Let's express this as an equation:

$2y-6=x$

Now we have a system of two equations. Let's add the two equations together:

$(x-y)+(2y-6)=(5)+(x)$

$rArrx+y-6=5+x$

Now we can eliminate $x$ and solve for $y$ .

$rArrcancelx-color(red)cancelx+y-6=5+cancelx-color(red)cancelx$

$rArry-6=5$

$rArry-cancel6+color(red)cancel6=5+color(red)6$

$rArry=11$

Now that we know $y$ , we can substitute it into our first equation:

$x-y=5$

$rArrx-11=5$

$rArrx-cancel11+color(red)cancel11=5+color(red)11$

$rArrx=16$

Let's check that our equations both hold true for
$x=16$ and $y=11$ :

$16-11=5$
$5=5$
Check!

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