Question

The sum of a three-digit number and one-digit number is 731. The product of the numbers is 2,908. What are the numbers?

Answer 1

Solving a system of equations we can see that the two numbers are 727 and 4

How to find the two numbers?

Let's define x as the 3-digit number and y as the one-digit number.

Then we know that the sum is equal to 731:

x + y = 731

And the product is equal to 2,908, then:

x*y = 2,908

So we have a system of equations:

x + y = 731

x*y = 2,908

Isolating x on the first equation gives:

x = 731 - y

Now we can replace that in the other equation to get:

(731 - y)*y = 2,908

Now we can solve this quadratic equation to find the value of y.

731*y - y^2 = 2,908

-y^2 + 731*y - 2,908 = 0

The solutions are:

y = (-731 ± √( 731^2 - 4*(-2,908)*(-1))/(-2)

y = (-731 ± 723)/-2

Now, y is an one digit number, then:

y = (-731 + 723)/-2 = 4

And x will be the 3 digit number:

x = 731 - x = 731 - 4 = 727

So the two numbers are 727 and 4

Learn more about systems of equations:

brainly.com/question/13729904

#SPJ1