If $X:Y: : 5:2$ then $9y:8x + 2y$ is equal to?

Given: $X:Y: : 5:2$ 

To do:  Find $9y:8x + 2y$ =?

Solution:

If $x:y =5 :2$, then (8x+9y):(8x+2y) =  ?

Let $x = 5k$ and $y = 2k$;

$\frac{x}{y} = \frac{5k}{2k} = \frac{5}{2}$

$(8x+9y):(8x+2y)$

=$\frac{8x+9y}{8x+2y}$

=$ \frac{8 \times 5k+ 9 \times 2k}{8 \times 5k + 2 \times 2k}$

= $\frac{40k + 18 k}{40k + 4k}$

= $\frac{58k}{44k}$

= $\frac{29}{22}$ or 29:22 

Therefore, the value of $9y:8x + 2y$ is $\frac{29}{22}$ or 29:22 

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Updated on: 10-Oct-2022

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