Question

Two numbers differ by 8 if their product is 713 then the sum of the two numbers is.

Answer 1

The sum of the two numbers is equal to 70.

• Let the first number be x.

• Let the second number be y.

In this exercise, you're required to find two numbers by translating the word problem into an algebraic expression and then solving for the unknown variables (x and y).

Translating the word problem into an algebraic expression, we have;

Two numbers differ by 8:

$x-y=8$    ....equation 1.

The product of the two numbers is 713:

$xy=713$    ....equation 2.

To calculate the sum of the two numbers:

First of all, we would solve for each of the unknown variables (x and y).

From eqn. 1, we have:

$x=8+y$   ....equation 3.

Substituting eqn. 3 into eqn. 2, we have:

$y(y+8)=713\\\\y^2+8y=713\\\\y^2+8y-713=0$

Solving the quadratic equation by factorization, we have:

$y^2-31y +23y-713=0\\\\y(y-31)+23(y-31)=0\\\\(y+23)(y-31)=0$

y = -23 or 31.

For the value of x, when y = 31:

$x=8+31$

x = 39

Now, we can calculate the sum of the two numbers:

$x+y=39+31=70$

Read more on word problems here: brainly.com/question/13170908