If a:b = 3:5 and b:c = 4:7, find a:c.

## The reasoning To connect a:c, we need a common "bridge" — and that bridge is **b**. Right now: - a:b = 3:5 means a = 3 parts, b = 5 parts - b:c = 4:7 means b = 4 parts, c = 7 parts **Problem:** b has different values (5 in the first ratio, 4 in the second). We need to make them equal. Find the **LCM of 5 and 4 = 20**. Scale the first ratio so b becomes 20: - a:b = 3:5 → multiply by 4 → **a:b = 12:20** Scale the second ratio so b also becomes 20: - b:c = 4:7 → multiply by 5 → **b:c = 20:35** Now b matches! So: **a:b:c = 12:20:35** Therefore: **a:c = 12:35** ## Why the wrong options tempt you **B) 15:28** — You might've added wrongly or used an incorrect LCM. **C) 3:7** — Classic trap: multiplying first numbers (3×1) and last numbers (5×7 ÷ 5). That's not how ratios link! **D) 5:7** — Just copying the second part of each ratio without connecting through b. ## Quick takeaway **Always equalize the "bridge" value using LCM when connecting ratios.**