Question

The difference of 2 numbers is 6 the sum of the numbers is 28 what are the 2 numbers?

Answer 1

The numbers are `11 and 17`

Explanation:

You can do this using either one variable or two.

Let's look at both methods.

Using ONE variable

Let the smaller number be `x`. The other number is `x+6`
(We know that because they differ by `6`. One is `6` more and the other is `6` less.)

The sum is `28`

`x +x+6=28`

`2x+6=28`
`2x = 28-6`
`2x = 22`
`x =11`

The numbers are `11 and 17`

Using TWO variables - you need TWO equations.

Let the numbers be `x and y`

`x-y=6" "rarr" "A`
`x+y=28" "rarr" "B`
`2x = 34" "larr" "A+B`
`x = 17`
`y = 17-6 = 11`

The numbers are `11 and 17`

Choose whichever method you find easier.

I prefer using one variable, but you have to know the relationship between the two numbers to be able to do that.

Answer 2

The two numbers are `color(red)(11 and 17`

Explanation:

Let the numbers be `x and y`

`:.x-y=6`------`(1)`

`:.x+y=28`------`(2)`

`:.(1)+(2)`

`:.2x=34`

`:.x=34/2`

`:.color(red)(x=17`

substitute `x=17` in `(1)`

`:.17-y=6`

`:.-y=6-17`

`-y=-11`

multiply both sides by `-1`

`:.color(red)(y=11`