Three-number chain ratios totaling 300: The sum of three numbers is 300. If the ratio between the first and second is 5:9 and the ratio between the second and third is 9:11, find the second number.

Introduction / Context:When two ratios share a common term (here the second number), they can be chained to produce a three-number proportion. With the total sum given, we can scale the base ratio to match the sum and extract the requested term.

Given Data / Assumptions:

• A:B = 5:9
• B:C = 9:11
• A + B + C = 300

Concept / Approach:Because B is common, align the ratios to 5:9 and 9:11 → the triplet is A:B:C = 5:9:11. Sum the parts, set equal to 300, solve for the scale factor, and compute B.

Step-by-Step Solution:A:B:C = 5:9:11 (since the 9s align)Total parts = 5 + 9 + 11 = 25Each part = 300 / 25 = 12Second number B = 9 * 12 = 108

Verification / Alternative check:Check totals: A = 60, B = 108, C = 132; sum = 300. Ratios A:B = 5:9 and B:C = 9:11 hold.

Why Other Options Are Wrong:12 and 60 are single-part or A values; 132 is C; 90 does not satisfy the chained ratios when scaled to 300.

Common Pitfalls:Mismatching the shared term when chaining ratios or adding parts incorrectly.

Final Answer:108