Question

if (7x-5y):(3x+4y)=7:11 then prove (3x-2y):(3x+4y)=137:473

Answer 1

Answer:

Step-by-step explanation:

Answer 2

(3x - 2y) : (3x + 4y) = 137 : 473, proved.

Step-by-step explanation:

We have,

(7x - 5y) : (3x + 4y) = 7 : 11

To prove that, (3x - 2y) : (3x + 4y) = 137 : 473.

∴ 7x - 5y = 7              ......(1)

Also,

3x + 4y = 11              ........(2)

Multiplying (1) by 4 and (2) by 5, we get

28x - 20y = 28         ......(3)

And,

15x + 20y = 55          ........(4)

Adding equations (3) and (4), we get

28x - 20y + 15x + 20y  = 28 + 55

⇒ 43x = 83

⇒ x = $\dfrac{83}{43}$

Putting the value of x in (1), we get

7($\dfrac{83}{43}$) - 5y = 7    

⇒ 5y = 7($\dfrac{83}{43}$) - 7

⇒ y = $\dfrac{56}{43}$

L.H.S. = (3x - 2y) : (3x + 4y)

= 3($\dfrac{83}{43}$) - 2($\dfrac{56}{43}$) : 3($\dfrac{83}{43}$) + 4($\dfrac{56}{43}$)

= $\dfrac{249-112}{43}:\dfrac{249+224}{43}$

= 137 : 473 = R.H.S., proved.

Thus, (3x - 2y) : (3x + 4y) = 137 : 473, proved.