Question

The sum of two numbers is 8, and their product is 15. What is the smaller number?

Answer 1

3 and 5

Explanation:

Begin by creating the two equations that are provided by the information in the question.

`x+y = 8`
and
`xy=15`

Now you can solve logically because of the simplicity of the numbers, by listing the factors of 15 and determine which pair will add up to 8

1 and 15
3 and 5

The Answer is 3 and 5

Or you can solve algebraically by substitution

`x + y =8` can be converted to

`y = 8 -x`

Now substitute the first equation into the second equation for the y variable.

`x(8-x) = 15`

Distribute

`8x - x^2 = 15`

Set the equation equal to zero.

`8x - x^2 - 15= cancel(15)cancel(-15)`

Rearrange to put the squared term first.

`-x^2+8x-15=0`

Factor the trinomial.

-1(x-5)(x-3) = 0#

Set both factors equal to zero.

`x-5=0`
`x=5`

`x-3=0`
`x=3`

`5 and 3`