Question

$if \: x:y = 3:4 , then (7x + 3y ):(7x -3y) =?​$
​

Answer 1

ANSWER:

Given:

• x : y = 3 : 4

To Find:

• (7x + 3y) : (7x - 3y)

Solution:

We are given that,

$\implies x : y = 3 : 4$

This can be written as,

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

METHOD 1:

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

Transposing y to RHS and 4 to LHS,

$\implies 4x=3y - - - - -(1)$

We need to find value of:

$\implies (7x + 3y) : (7x - 3y)$

$\implies \dfrac{7x + 3y}{7x - 3y}$

Substituting the value of 3y,

$\implies \dfrac{7x + 4x}{7x - 4x}$

$\implies \dfrac{11x}{3x}$

Cancelling x,

$\implies\bf\dfrac{11}{3}$

METHOD 2:

$\implies \dfrac{x}{y}=\dfrac{3}{4} - - - - -(2)$

We need to find value of:

$\implies (7x + 3y) : (7x - 3y)$

$\implies \dfrac{7x + 3y}{7x - 3y}$

Dividing the numerator and denominator by y,

$\implies \dfrac{\dfrac{7x + 3y}{y}}{\dfrac{7x - 3y}{y}}$

$\implies \dfrac{\dfrac{7x}{y}+ 3}{\dfrac{7x}{y} - 3}$

$\implies \dfrac{7\left(\dfrac{x}{y}\right)+ 3}{7\left(\dfrac{x}{y}\right) - 3}$

Substituting the value of x/y,

$\implies \dfrac{7\left(\dfrac{3}{4}\right)+ 3}{7\left(\dfrac{3}{4}\right) - 3}$

$\implies \dfrac{\dfrac{21}{4}+ 3}{\dfrac{21}{4} - 3}$

$\implies \dfrac{\dfrac{21+12}{4}}{\dfrac{21-12}{4}}$

$\implies \dfrac{33}{9}$

$\implies\bf\dfrac{11}{3}$

Hence,

$\implies\bf (7x + 3y) : (7x - 3y) = 11 : 3$