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Finding the Third Proportional to 9,709 and 15,397.50

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Solution

The third proportional to 9,709 and 15,397.50 is: 24,418.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,709 : 15,397.50 = 15,397.50 : x
  2. Step 2: Convert to fraction form
    9,709/15,397.50 = 15,397.50/x
  3. Step 3: Cross multiply
    9,709x = 15,397.50 × 15,397.50
  4. Step 4: Simplify right side
    9,709x = 237,083,006.25
  5. Step 5: Solve for x
    x = 237,083,006.25/9,709
  6. Step 6: Final answer
    x = 24,418.89

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.