a.b.
If (7x-5y):(3x+4y)=7:11, let us show that, (3x-2y):(3x+4y)=127:473
Answers
Answer:
(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}
43
83
Putting the value of x in (1), we get
7(\dfrac{83}{43}
43
83
) - 5y = 7
⇒ 5y = 7(\dfrac{83}{43}
43
83
) - 7
⇒ y = \dfrac{56}{43}
43
56
L.H.S. = (3x - 2y) : (3x + 4y)
= 3(\dfrac{83}{43}
43
83
) - 2(\dfrac{56}{43}
43
56
) : 3(\dfrac{83}{43}
43
83
) + 4(\dfrac{56}{43}
43
56
)
= \dfrac{249-112}{43}:\dfrac{249+224}{43}
43
249−112
:
43
249+224
= 137 : 473 = R.H.S., proved.
Thus, (3x - 2y) : (3x + 4y) = 137 : 473, proved.