a:(b+c)=5:7 c:(a+b)=2:3 then (a=2b):(b+2c)=?

Question

please resolve

Answer 1

a/(b+c) = 5/7      c/(a+b) = 2/3

 

So, 5b+5c = 7a   and   3c = 2a+2b

 

5c = 7a-5b  so, c = (7/5)a - b 

 

Since 3c = 2a+2b, c = (2/3)a + (2/3)b

 

Therefore, (7/5)a - b = (2/3)a + (2/3)b

 

                (11/15)a = (5/3)b    So, b = (3/5)(11/15)a = (11/25)a

 

                c = (2/3)a + (2/3)b = (2/3)a + (11/25)a = (83/75)a

 

So, (a+2b) / (b+2c) = [a + (22/25)a] / [(11/25)a + (166/75)a]

 

                              = [(47/25)a] / [(199/75)a] = (47/25)(75/199) = 141/199