Question

Please solve this question. ​

Answer 1

Let numerator of fraction be x and denominator be y.

∴ Fraction = x/y

★ Part - A :

`:\implies\tt\:(x* 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)`

★ Part - B :

`:\implies\tt\:(x+15)/(2y-2)=(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=(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

Hope It Helps!

Answer 2

Answer: 3/8

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