Question

Question #164a5

Answer 1

`4", "16"`

Explanation:

Let the two numbers be `a` and `b`.

Set up a system of equations:
`a+b=20` and
`a*b=64`

We get a quadratic equation and a linear equation here. Try solving for `a` and `b` one at a time, by replacing either of the variables in the quadratic equation using expression derived from the linear one. Here I choose to replace `b` in the second equation with an expression of `a`:
`b=20-a`

Replace `b` with `(20-a)`:
`a*(20-a)=64`

Simplify, factor, and solve:
`-a^2+20a-64=0`
`(a-4)(a-16)=0`

Therefore `a=4` or `a=16` while `b=16` or `b=4`, respectively.
So the two numbers are `4` and `16`

Answer 2

The numbers are `4 and 16`

Explanation:

We can use one variable to define the two variables.

Let the smaller number be `x`.

The sum of the numbers is `20`.

If one number is `x`, the other is `(20-x)`

Their product is `64`

`x(20-x) =64`

`20x-x^2 =64" "larr`make equal to `0`

`0 = x^2 -20x+64`

Factor of `64` which add to `20` are `4 and 16`

`(x-4)(x-16)=0`

Setting each factor equal to `0` gives: `x=4 and x=16`

If `x=4`, the other number is `16`