Question

x/6 = y/5 = 5x+3y / ? = 11x-9y/ ?​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \frac{x}{6} = \frac{y}{5} = \frac{5x + 3y}{?} = \frac{11x - 9y}{?} }$

TO DETERMINE

The value in ? mark

EVALUATION

Let

$\displaystyle \sf{ \frac{x}{6} = \frac{y}{5} = \frac{5x + 3y}{m} = \frac{11x - 9y}{n} = k }$

Which gives

x = 6k - - - - (1)

y = 5k - - - - - (2)

5x + 3y = mk - - - - (3)

11x - 9y = nk - - - - - (4)

From Equation 3 we get

30k + 15k = mk

$\implies \sf{mk = 45k}$

$\implies \sf{m = 45}$

Again Equation 4 gives

66k - 45k = nk

$\implies \sf{nk = 21k}$

$\implies \sf{n = 21}$

Hence

$\displaystyle \sf{ \frac{x}{6} = \frac{y}{5} = \frac{5x + 3y}{45} = \frac{11x - 9y}{21} }$

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