Question

If \(a : b = 3 : 4\) and \(b : c = 8 : 9\), then \(a : c\) is

• A. 1 : 3
• B. 3 : 2
• C. 1 : 2
• D. 2 : 3

Hint:

When combining ratios, make sure the common terms are equal before combining the ratios.

Answer 1

The Correct Option is C

We know: \[\na : b = 3 : 4 \quad \text{and} \quad b : c = 8 : 9\n\] To find \(a : c\), adjust the ratios so the value of \(b\) is the same. The least common multiple (LCM) of 4 and 8 is 8. Multiply the first ratio by 2: \[\na : b = 6 : 8 \quad \text{and} \quad b : c = 8 : 9\n\] Combine the ratios: \[\na : c = 6 : 9 = 2 : 3\n\] Therefore, \(a : c = 2 : 3\).