If 6a = 3b = 7c and 5b = 8a + 4c, what is the value of a + b + c?

Question

How to approach this question??

Akshat · Accepted Answer

Start with 6a = 3b = 7c. The least common multiple of 6, 3, and 7 is 42, so we can write: 6a = 3b = 7c = 42x, for some number x. Thus, a = 7x, b = 14x, and c = 6x.
Substituting these values into 5b = 8a + 4c we get:
5(14x) = 8(7x) + 4(6x);70x = 56x + 24x;70x = 80x;
Subtracting 70x from both sides:0 = 10x;
Solving for x:x = 0.
As x = 0, we find that a = 7x = 0,b = 14x = 0, and c = 6x = 0.
Therefore, a + b + c = 0 + 0 + 0 = 0.