1, The Sum of a number x and twice another is 20. If the product of these number is not more than 48, what are all possible values of x?
3 answers
I don’t know
Mark first and second number x and y
x + 2 y = 20
Subtract 2 y to both sides
x = 20 - 2 y
x ∙ y = 48
Replace x by 20 - 2 y in this equation
( 20 - 2 y ) ∙ y = 48
20 y - 2 y² = 48
Subtract 48 to both sides
- 2 y² + 20 y - 48 = 0
Divide both sides by - 2
y² - 10 y + 24 = 0
The solutions of this quadratic equations are;
y = 4 and y = 6
For y = 4
x = 20 - 2 y = 20 - 2 ∙ 4 = 20 - 8 = 12
For y = 6
x = 20 - 2 y = 20 - 2 ∙ 6 = 20 - 12 = 8
You can write the solutions as:
( 8 , 6 ) , ( 12 , 4 )
Where first number is x coordinate, second number is y coordinate.
x + 2 y = 20
Subtract 2 y to both sides
x = 20 - 2 y
x ∙ y = 48
Replace x by 20 - 2 y in this equation
( 20 - 2 y ) ∙ y = 48
20 y - 2 y² = 48
Subtract 48 to both sides
- 2 y² + 20 y - 48 = 0
Divide both sides by - 2
y² - 10 y + 24 = 0
The solutions of this quadratic equations are;
y = 4 and y = 6
For y = 4
x = 20 - 2 y = 20 - 2 ∙ 4 = 20 - 8 = 12
For y = 6
x = 20 - 2 y = 20 - 2 ∙ 6 = 20 - 12 = 8
You can write the solutions as:
( 8 , 6 ) , ( 12 , 4 )
Where first number is x coordinate, second number is y coordinate.
Of course all possible values of x are x = 8 and x = 12