Three numbers add up to 172. The ratio between the first and second numbers is 8 to 11, while the ratio between the second and third numbers is 5 to 7. What is the value of the second number?

Explanation

Let the three numbers be a, b, and c. Given a + b + c = 172, with ratios a:b = 8:11 and b:c = 5:7. From a:b = 8:11, we get a = (8/11) * b. From b:c = 5:7, we have c = (7/5) * b. Substituting into the sum: (8b/11) + b + (7b/5) = 172. Multiplying through by 55 (LCM of 11 and 5) gives 40b + 55b + 77b = 172 * 55, which simplifies to 172b = 9460. Solving for b yields b = 55.