Find the numbers

Question

one number is 5 less than 3 times another number. the product of the number is 50. Find the numbers 

Answer 1

Hi Evan, let x represent the number. Then the equation to find the value of x is:

 

x * (3x  - 5) = 50

 

Solve for x:

 

3x² - 5x = 50

 

Subtract 50 from both sides:

 

3x² -5x - 50 = 0

 

Factor:

 

Factors for 3 are: 3 and 1.

 

Factors for 50 are:

 

1 and 50

 

2 and 25

 

5 and 10

 

Factoring the equation gives:

 

3x² - 5x - 50 = (x - 5) * (3x + 10) = 0

 

Use the zero product rule:

 

x - 5 = 0

 

x = 5

 

And

 

3x + 10 = 0

 

x = -10/3

 

The solution has two numbers, 5 and -10/3.

 

Check:

 

Substitute 5 into original equation:

 

5 * (3 * 5 - 5) = 50

 

5 * (15 - 5) = 50

 

5 * 10 = 50

 

50 = 50

 

Substitute -10/3 into original equation:

 

-10/3 * (3 * -10/3 - 5) = 50

 

-10/3 * (-15) = 50

 

-10 * -5 = 50

 

50 = 50

 

Values check.

 

Questions?