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Ganezh [65]
3 years ago
9

Please solve this question. ​

Mathematics
2 answers:
egoroff_w [7]3 years ago
5 0
<h3><u>Answer</u> :</h3>

Let numerator of fraction be x and denominator be y.

∴ Fraction = x/y

★ <u>Part - A</u> :

:\implies\tt\:\dfrac{x\times 4}{y-2}=2

:\implies\tt\:4x=2(y-2)

:\implies\tt\:4x=2y-4

:\implies\tt\:2y=4x+4

:\implies\bf\:y=2x+2\:\:\dots (1)

★ <u>Part</u><u> </u><u>-</u><u> </u><u>B</u> :

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

:\implies\tt\:7(x+15)=9(2y-2)

:\implies\tt\:7x+105=18y-18

From equation (1)...

:\implies\tt\:7x+105=18(2x+2)-18

:\implies\tt\:7x+105=36x+38-18

:\implies\tt\:29x=105-18

:\implies\tt\:x=\dfrac{87}{29}

:\implies\boxed{\bf{x=3}}

:\implies\tt\:y=2x+2

:\implies\tt\:y=2(3)+2

:\implies\boxed{\bf{y=8}}

∴ Fraction = x/y = 3/8

<h3>Hope It Helps!</h3>
nika2105 [10]3 years ago
3 0

Answer:  3/8

<u>Step-by-step explanation:</u>

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)  →     <u>  -7x + 18y</u> = <u>123  </u>

                                                                              29x          =  87

                                                                           <u> ÷29    </u>          <u>÷29 </u>

                                                                                  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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