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Finding the Third Proportional to 14,309 and 31,306

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Solution

The third proportional to 14,309 and 31,306 is: 68,492.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,309 : 31,306 = 31,306 : x
  2. Step 2: Convert to fraction form
    14,309/31,306 = 31,306/x
  3. Step 3: Cross multiply
    14,309x = 31,306 × 31,306
  4. Step 4: Simplify right side
    14,309x = 980,065,636
  5. Step 5: Solve for x
    x = 980,065,636/14,309
  6. Step 6: Final answer
    x = 68,492.95

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.