Question

If a/b=c/d, then show that
a-4c/b-4d=3a-7c/3b-7d​

Answer 1

Given : a/b=c/d,

To Find : show that

a-4c/b-4d=3a-7c/3b-7d​

Solution:

Let say a/b=c/d = k

=> a = bk  , c  = dk

(a-4c)/(b-4d)=(3a-7c)/(3b-7d)​

LHS =  (a - 4c)/(b - 4d)

= (bk - 4dk)/(b - 4d)

= k(b - 4d)/(b - 4d)

= k

RHS = 3a-7c/3b-7d​

= (3bk - 7dk) / (3b - 7d)

= k(3b - 7d)/(3b - 7d)

= k

LHS = RHS = k

Hence proved

(a-4c)/(b-4d)=(3a-7c)/(3b-7d)​

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Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ \frac{a}{b} = \frac{c}{d} }$

TO PROVE

$\displaystyle \sf{ \frac{a - 4c}{b - 4d} = \frac{3a - 7c}{3b - 7d} }$

EVALUATION

$\displaystyle \sf{ \frac{a}{b} = \frac{c}{d} }$

$\displaystyle \sf{ Let \: \: \: \frac{a}{c} = \frac{b}{d} = k}$

$\displaystyle \sf{ \implies \: a = kc \: \: \: and \: \: \: b = kd}$

Now

LHS

$\displaystyle \sf{ = \frac{a - 4c}{b - 4d} }$

$\displaystyle \sf{ = \frac{kc- 4c}{kd - 4d} }$

$\displaystyle \sf{ = \frac{c(k- 4)}{d(k - 4)} }$

$\displaystyle \sf{ = \frac{c}{d} }$

RHS

$\displaystyle \sf{ = \frac{3a - 7c}{3b - 7d} }$

$\displaystyle \sf{ = \frac{3kc - 7c}{3kd- 7d} }$

$\displaystyle \sf{ = \frac{(3k - 7)c}{(3k- 7)d} }$

$\displaystyle \sf{ = \frac{c}{d} }$

Hence LHS = RHS

Hence proved

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