16Hit1600
Problem-Solving and Data AnalysisVery hardCombining two ratios

Problem-Solving and Data Analysis practice question

The ratio of a to b is 3 : 4, and the ratio of b to c is 6 : 5. What is the ratio of a to c?

  1. A. 9 : 10Correct
  2. B. 3 : 5
  3. C. 9 : 20
  4. D. 18 : 5

Answer: A. 9 : 10

a/c = (a/b) × (b/c) = (3/4) × (6/5) = 18/20 = 9/10. Equivalently, scale both ratios so b matches: a : b = 9 : 12 and b : c = 12 : 10, so a : c = 9 : 10.

Why the other answers are wrong

B. 3 : 5
3 : 5 just takes the first number of one ratio and the last of the other. The shared quantity b has to be matched up first (b = 12 in both).
C. 9 : 20
9 : 20 scales a : b to 9 : 12 but leaves c at 20 instead of scaling it to 10.
D. 18 : 5
18 : 5 multiplies the a-values (3 × 6) without adjusting c; the ratio of a to c is 18 : 20 = 9 : 10.

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