Question

given 4725=3a 5b 7c, find the values of a, b,c

Answer 1

a+b:b+c:c+a=6:7:8

(a+b)/(b+c)=6/7
=> 7(a+b)=6(b+c)
solving it, we get
b=6c-7a------------(1)
then,
(b+c)/(c+a)=7/8
=> 8(b+c)=7(a+c)
solving it, we get
c=7a-8b---------------(2)

substituting the value of c in (1),
b=6(7a-8b)-7a
=>b=42a-48b-7a
solving it, we get
49b=35a
=> a/b=7/5--------------(3)

now, take eqn (2)
c=7a-8b
=>c/b=7(a/b)-8
=7*(7/5)-8
=9/5
b/c=5/9------------------(4)

combining (3) &(4)
we get,
a:b:c=7:5:9(ans)