The total of three numbers is 98. Given that the ratio of the first number to the second is 2 to 3, and the ratio of the second number to the third is 5 to 8, what is the value of the second number?

Explanation

Let the three numbers be A, B, and C. From the given ratios, A : B = 2 : 3 and B : C = 5 : 8. To combine these, express B in terms of a common ratio: A : B : C = 2 : 3 : (8 × 3/5) = 2 : 3 : 4.8. Multiplying all by 5 to clear decimals gives 10 : 15 : 24. The sum is 10 + 15 + 24 = 49 parts. Since the total is 98, each part equals 2. Therefore, the second number B = 15 × 2 = 30.