KnowledgeBoat Logo
|

Mathematics

If (5x + 2y) : (7x + 4y) = 13 : 20, find x : y.

Ratio Proportion

2 Likes

Answer

Given,

(5x + 2y) : (7x + 4y) = 13 : 20,

⇒5x+2y7x+4y=1320⇒20(5x+2y)=13(7x+4y)⇒100x+40y=91x+52y⇒100x−91x=52y−40y⇒9x=12y⇒xy=129⇒xy=43.\Rightarrow \dfrac{5x + 2y}{7x + 4y} = \dfrac{13}{20} \\[1em] \Rightarrow 20(5x + 2y) = 13(7x + 4y) \\[1em] \Rightarrow 100x + 40y = 91x + 52y \\[1em] \Rightarrow 100x - 91x = 52y - 40y \\[1em] \Rightarrow 9x = 12y \\[1em] \Rightarrow \dfrac{x}{y} = \dfrac{12}{9} \\[1em] \Rightarrow \dfrac{x}{y} =\dfrac{4}{3}.

Hence, x : y = 4 : 3.

Answered By

1 Like

Related Questions