Question

If , (4x + 3y) : (3x + 4y) = 24 : 25 , find the value of x : y .

Answer 1

We have ( 4x + 3y ) : ( 3x + 4y ) = 24 : 25

$\\ \sf\longmapsto \: \frac{4x + 3y}{3x + 4y} = \frac{24}{25}$

$\\ \sf\longmapsto \: 25(4x + 3y) = 24(3x + 4y)$

$\\ \sf\longmapsto \: 100x + 75y = 72x + 96y$

$\\ \sf\longmapsto \: 100x - 72x = 96y - 75y$

$\\ \sf\longmapsto \: 28x = 21y$

$\\ \sf\longmapsto \: \frac{x}{y} = \frac{21}{28} = \frac{3}{4}$

Hence ,

• x : y = 3 : 4

Answer 2

$\\ \sf\longmapsto \dfrac{4x+3y}{3x+4y}=\dfrac{24}{25}$

• Use cross multiplication

$\\ \sf\longmapsto 24(3x+4y)=25(4x+3y)$

$\\ \sf\longmapsto 72x+96y=100x+75y$

$\\ \sf\longmapsto 96y-75y=100x-72x$

$\\ \sf\longmapsto 21y=28x$

$\\ \sf\longmapsto \dfrac{x}{y}=\dfrac{21}{28}$

• Cut 7

$\\ \sf\longmapsto \dfrac{x}{y}=\dfrac{3}{4}$

$\\ \sf\longmapsto x:y=3:4$