Explanation

Given:

a : b : c = 2 : 5 (let's assume a common multiple for b and c to match both ratios)

b : c = 3 : 7

To match both ratios, let's find the LCM for b in both ratios.

Given a : b = 2 : 5 and b : c = 3 : 7, let's make the ratios comparable by finding a common multiple for b.

For a : b = 2 : 5 and b : c = 3 : 7,

let's scale a : b : c = 2_3 : 5_3 : 5*7 = 6 : 15 : 35

Now b : c = 15 : 35 which simplifies to 3 : 7.

Given a : b : c = 6 : 15 : 35

a : c = 6 : 35