Problem: A number is 8 more than another number if the product of the two numbers is 20. Find the numbers.

First number: x

Second Number: y (or x + 8)

First Equation: xy = 20

Second Equation: y = x+8

In terms of one variable "x", substitute the x+8 of second equation in y in Equation 2:

x (x + 8) = 20

x² + 8x = 20

Arrange in standard form of quadratic equation:

x² + 8x - 20 = 0

Check if this can be factored by finding the discriminant:

a = 1 b = 8 c = -20

Discriminant: b² - 4ac

= (8)² - 4(1)(-20)

= 64 + 80

= 144

Since discriminant is more than 0, that is, 144>0, we can use factoring to solve the equation instead of other method.

x² + 8x - 20 = 0

Factor:

(x + 10) (x - 2) = 0

x + 10 = 0 x - 2 = 0

x = -10 x = 2

Check:

First number: **2**

Second Number: 2 + 8 = **10**

**ANSWER: The numbers are 2 and 10.**

Note: I include the explanation so you can recite and defend your answer with solution. Good luck!