Question

If x:y = 3:8, then find the value of (5x + 7y):(8x + 11y).

Explain with Solution​

Answer 1

Step-by-step explanation:

Given, x:y = 3:8

hence, x=3 and y=8

put these values in given expression we get,

(5.3+7.8):(8.3+11.8)

=(15+56):(24+88)

=71:112 ans

Answer 2

ANSWER :-

• Required answer is 71/112.

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GIVEN :-

• x:y = 3:8

TO FIND :-

• (5x + 7y) : (8x + 11y)

SOLUTION :-

As x and y in ratio of 3:8 , let x be 3k and y be 8k.

Now , we will substitute these values ...

$\\ \\ \sf \: \dfrac{5x + 7y}{8x + 11y} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: \dfrac{5(3k) + 7(8k)}{8(3k) + 11(8k)} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: \dfrac{15k + 56k}{24k + 88k} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: \dfrac{71 \cancel{k}}{112 \cancel{k} } \\ \\ \\ \implies \sf \: \underline{\boxed{ \sf\dfrac{5x + 7y}{8x + 11y} = \dfrac{71}{112} }}$

VERIFICATION :-

$\\ \sf \: \dfrac{5x + 7y}{8x + 11y} = \dfrac{71}{112} \\ \\ \\ \implies \sf \: 112(5x + 7y) = 71(8x + 11y) \\ \\ \implies \sf \: 560x + 784y = 568x + 781y \\ \\ \implies \sf \: 560x - 568x = 781y - 784y \\ \\ \implies \sf \: \cancel- \: 8x = \cancel- \: 3y \\ \\ \implies \sf \: 8x = 3y \\ \\ \implies \sf \: \boxed{ \sf\dfrac{x}{y} = \dfrac{3}{8} } \: \: \: \: \: (verified)$