Question

The product of two whole number is 462 and their sum is 43. What are the two numbers?

Answer 1

Answer:

21 and 22

Step-by-step explanation:

Let's let the numbers be a and b.

Their product is 462, in other words:

$ab=462$

Their sum is 43, in other words:

$a+b=43$

We now have a system of equations. We can solve by substitution.

First, let's subtract both sides by b in the second equation:

$a=43-b$

Substitute this into the first equation:

$(43-b)(b)=462$

Distribute:

$-b^2+43b=462$

Divide everything by -1:

$b^2-43b=-462$

Add 462 to both sides:

$b^2-43b+462=0$

Factor. We can use -21 and -22:

$(b-21)(b-22)=0$

Zero Product Property:

$b=21\text{ or } b=22$

Substitute this into the second equation again:

$a=43-(21)\text{ or } a=43-(22)\\a=22\text{ or } a=21$

It doesn't matter which one we chose, but the numbers are 21 and 22.

And we're done!

Answer 2

Answer:22 and 21

Step-by-step explanation: