Answer :

BrainlyWarrior

Answer :

Let numerator of fraction be x and denominator be y.

∴ Fraction = x/y

★ Part - A :

[tex]:\implies\tt\:\dfrac{x\times 4}{y-2}=2[/tex]

[tex]:\implies\tt\:4x=2(y-2)[/tex]

[tex]:\implies\tt\:4x=2y-4[/tex]

[tex]:\implies\tt\:2y=4x+4[/tex]

[tex]:\implies\bf\:y=2x+2\:\:\dots (1)[/tex]

★ Part - B :

[tex]:\implies\tt\:\dfrac{x+15}{2y-2}=\dfrac{9}{7}[/tex]

[tex]:\implies\tt\:7(x+15)=9(2y-2)[/tex]

[tex]:\implies\tt\:7x+105=18y-18[/tex]

From equation (1)...

[tex]:\implies\tt\:7x+105=18(2x+2)-18[/tex]

[tex]:\implies\tt\:7x+105=36x+38-18[/tex]

[tex]:\implies\tt\:29x=105-18[/tex]

[tex]:\implies\tt\:x=\dfrac{87}{29}[/tex]

[tex]:\implies\boxed{\bf{x=3}}[/tex]

[tex]:\implies\tt\:y=2x+2[/tex]

[tex]:\implies\tt\:y=2(3)+2[/tex]

[tex]:\implies\boxed{\bf{y=8}}[/tex]

∴ Fraction = x/y = 3/8

Hope It Helps!

tramserran

Answer:  3/8

Step-by-step explanation:

Let x represent the numerator and y represent the denominator.

Equation 1: (4x)/(y - 2) = 2

                  4x = 2(y - 2)        Cross Multiplied

                  4x = 2y - 4           Distributed

                  4x - 2y = -4          Subtracted 2y from both sides

Equation 2: (x + 15)/(2y - 2) = 9/7

                  9(2y - 2) = 7(x+15)           Cross Multiplied

                  18y - 18 = 7x + 105          Distributed

                  -7x + 18y - 18  = 105        Subtracted 7x from both sides

                  -7x + 18y = 123                Added 18 to both sides

Solve the system of equations using Elimination Method:

EQ1:    4x - 2y =  -4     →    9(4x - 2y =  -4)     →      36x - 18y =  -36

EQ2: -7x + 18y = 123   →   1(-7x + 18y = 123)  →      -7x + 18y = 123  

                                                                              29x          =  87

                                                                            ÷29              ÷29

                                                                                  x         =  3

Substitute x = 3 into either equation to solve for y:

EQ1: 4x - 2y = -4

      4(3) - 2y = -4

       12  - 2y = -4

            -2y  = -16

              y  =   8

The numerator (x) = 3

The denominator (y) = 8

The fraction is: 3/8

       

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