Question

x:y =3:4 find(4x +5y) : (5x-2y)​

Answer 1

Given :

x : y = 3 : 4 =≥ Equation 1

To find : (4x+5y) : (5x-2y) =≥ Equation 2

by expressing the ratios in fraction form :

Equation 1 :

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

by cross Multiplication,

$4x = 3y$

transposing 4 to the RHS (Right Hand Side)

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

Equation 2 :

Substituting the value of x we got from equation 1,

$\dfrac{4x + 5y}{5x - 2y}$

$\dfrac{4( \frac{3y}{4}) + 5y}{5( \frac{3y}{4}) - 2y}$

by multiplying we get :

$\dfrac{3y + 5y}{ \frac{15y}{4} - 2y}$

$\dfrac{8y}{ \frac{15y - 8y}{4} }$

$\dfrac{8y}{ \frac{7y}{4} }$

$8y \div (\dfrac{7y}{4})$

$8y \times \dfrac{4}{7y}$

y gets cancelled in the numerator and the denominator

$\dfrac{8 \times 4}{7}$

$= \dfrac{32}{7}$

By expressing as ratio,

Answer =≥ 32 : 7