Question

The average of two numbers is 50. Their difference is 40, how do you write an equation that may be used to find x the smallest of the two numbers?

Answer 1

`x=30`

Explanation:

You know that you need to find two numbers, `x` and let's say `y`.

The average of two numbers is equal to their sum divided by `2`, so your first equation will be

`(x+y)/2 = 50`

The difference between `y` and `x`, since `x` is the smallest of the two, is equal to `40`, which means that your second equation will be

`y - x = 40`

You thus have a system of two equations

`{( (x+y)/2 = 50), (y-x=40) :}`

To solve for `x`, use the first equation to express `y` as a function of `x`

`(x+y)/2 = 50 <=> x+y = 100 => y = 100 -x`

Plug this into the second equation to get

`(100-x) -x = 40`

`color(blue)(100 - 2x = 40)` `->` this is the equation that will get you `x`.

The value of `x` will be

`2x = 60 => x = color(green)(30)`

The value of `y` will be

`y = 100 - 30 = color(green)(70)`