Question

If the sum of two numbers is 50 and their mean proportional is 15 then the numbers are

Answer 1

Mean proportional of two positive number, say "a" and "b" is define as follow:

a/x = x/b where x is the mean proportional

Define x:

Let x be one of the number

The other number is (50 - x)

Solve x:

$\dfrac{x}{15} = \dfrac{15}{50 - x}$

$x(50 - x) = 15 \times 15$

$x(50 - x) = 225$

$50x - x^2 - 225 = 0$

$x^2 - 50x + 225 = 0$

$(x - 5) (x - 45) = 0$

$x = 5 \ \ or \ \ x = 45$

Answer: The two numbers are 5 and 45

Answer 2

Mean relative of two positive number, say "an" and "b" is characterize as take after:

a/x = x/b where x is the mean corresponding Define x:

Let x be one of the number The other number is (50 - x) Solve x: \dfrac{x}{15} = \dfrac{15}{50 - x} x(50 - x) = 15 \times 15 x(50 - x) = 225 50x - x^2 - 225 = 0 x^2 - 50x + 225 = 0 (x - 5) (x - 45) = 0 x = 5 \ or \ x = 45 Answer: The two numbers are 5 and 4.