The sum of three numbers is 98. If first:second = 2:3 and second:third = 5:8, find the second number.

Problem restatement
Three numbers have chained ratios; determine the second number given the total is 98.

Given data

• First:Second = 2:3
• Second:Third = 5:8
• Sum = 98

Concept/Approach
Convert chained ratios to a single triplet by matching the common term (the second number) and then scale to the total.

Step-by-step calculation
Let First:Second = 2k:3k; Second:Third = 5m:8mMatch seconds: 3k = 5m ⇒ k = 5t, m = 3tTriplet = First:Second:Third = 10t : 15t : 24tSum = 49t = 98 ⇒ t = 2Second = 15t = 30

Verification/Alternative
Numbers are 20, 30, 48; sums to 98 and ratios check out.

Common pitfalls
Adding the two ratios directly instead of linking via the common second term.

Final Answer
30