Question

A
If (5a - 3b): (4a - 2b) = 2:3, then a:b is equal to:​

Answer 1

Given:-

(5a-3b):(4a-2b)=2:3

To find:-

a:b

Solution:-

$\\ \rm\longmapsto (5a-3b):(4a-2b)=2:3$

$\\ \rm\longmapsto \dfrac{5a-3b}{4a-2b}=\dfrac{2}{3}$

• Use cross multiplication

$\\ \rm\longmapsto 3(5a-3b)=2(4a-2b)$

$\\ \rm\longmapsto 15a-9b=8a-4b$

$\\ \rm\longmapsto 15a-8a=-4b+9b$

$\\ \rm\longmapsto 7a=5b$

$\\ \rm\longmapsto \dfrac{a}{b}=\dfrac{5}{7}$

$\\ \rm\longmapsto \underline{\boxed{\bf{a:b=5:7}}}$

Answer 2

Step-by-step explanation:

a : b = 5 : 7

Given :

(5a - 3b) : (4a - 2b) = 2 : 3

To Find -

a : b

$\bf \huge \underline \green{solution}$

$\bf \large\frac{5a - 3b}{4a - 2b} = \frac{2}{3}$

$\bf \large 3(5a - 3b) = 2(4a - 2b)$

$\bf \large \: 15a - 9b = 8a - 4b$

$\bf \large \: 15a - 8a = - 4b + 9b$

$\bf \large \: 7a = 5b$

$\bf \large \: \frac{a}{b} = \frac{5}{7}$

$\bf \large \: \: a : b = 5 : 7$