Question

Find two numbers if their ratio is 9:11 and their difference is 6. Not 27 and 33

Answer 1

Answer:

 Sets of numbers are ( 27,33) and (-27, -33)

Explanation;

   Let the numbers be a and b.

  We have their ratio is 9:11

            $\frac{a}{b} =\frac{9}{11} \\ \\11a=9b$

  Their difference is 6

         $\left | a- \right b|=7$

       ( a - b) = 6 or      (b - a ) = 6

       11a - 11 b = 66   or   11b - 11a = 66

       9b - 11 b = 66   or  11b -9b = 66

             -2b = 66   or    2b = 66

                 b = -33 or b = 33

        if b = -33, a = -33 + 6 = -27

        if b = 33, a = 33-6 =27

     So, the sets of numbers are ( 27,33) and (-27, -33)

Answer 2

The two numbers must be 10.909 and 22.091.

According to the statement, two numbers must satisfy the following expressions:

$y-x = 6$ (1)

$\frac{x}{y} = \frac{9}{9+11}$ (2)

Then, the solution of the system of equations is:

$y-\frac{9}{20}\cdot y = 6$

$\frac{11}{20}\cdot y = 6$

$y = 10.909$

$x = 22.091$

The two numbers must be 10.909 and 22.091.

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