Question

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

Answer 1

The two numbers are 16 and 11.

Explanation:

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!