Question

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?

Answer 1

`x = 13`
`y = 31`

Explanation:

You have two unknown numbers, we shall name them `x` and `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`, is 5 more than twice the first. To represent this, we write
`y = 2x + 5`
where `2x` comes from 'twice the first', and
`+5` comes from '5 more'.

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

Now we have two equations to work off.

To find `x`, substitute `y = 2x + 5` into `x+y = 44`.
We then get
`x + (2x + 5) = 44`
`3x + 5= 44`
`3x = 44 - 5`
`3x = 39`
`x = 39/3`
`x = 13`

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