Question

Find a:b:c,given 3a+2b=7c and b=a+c​

Answer 1

$\bf\purple{QuestioN:-}$

Find a:b:c, given 3a + 2b = 7c and b = a + c​.

$\bf\pink{AnsweR:-}$

GiveN:-

3a + 2b = 7c

b = a + c

To FinD:-

a : b : c = ??

SolutioN:-

It is given that, b = a + c

$\longmapsto\bf{3a+2b=7c}$

Instead of b we can substitute, a + c

$\longmapsto\bf{3a+2(a+c)=7c}$

$\longmapsto\bf{3a+2a+2c=7c}$

$\longmapsto\bf{5a=7c-2c}$

$\longmapsto\bf{5a=5c}$

Then,

$\longmapsto\bf{a:c=1:1}$

Then instead of 7c we can write as 7a. Then,

$\longmapsto\bf{3a+2b=7a}$

$\longmapsto\bf{2b=7a-3a}$

$\longmapsto\bf{2b=4a}$

Then,

$\longmapsto\bf{a:b=4:2=2:1}$

As we know,

a = c = 1/2 b

2a = 2c = b

Then,

$\longmapsto\bf{a:b:c=2:1:2}$

The required ratio is, 2 : 1 : 2

Happy Learning!!

Answer 2

Answer:

3a+2b=7c

or 2b=7c-3a  

orb=(7c-3a)/2--------(1)  

put value of b in equation  

b=a+c

(7c-3a)/2=a+c

7c-3a=2a+2c

or 7c-2c=2a+3a

or 5c = 5a

or c=a

put c=a in equation (1)

b=(7a-3a)/2

or b=4a/2

b=2a

therefore

a:b:c = 1:2:1

Step-by-step explanation:

thanks..

Have a nice day.