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  • Brainly User
2016-06-18T18:57:15+08:00
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!
2 5 2
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