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Finding the Third Proportional to 7,778 and 10,209

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Solution

The third proportional to 7,778 and 10,209 is: 13,399.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,778 : 10,209 = 10,209 : x
  2. Step 2: Convert to fraction form
    7,778/10,209 = 10,209/x
  3. Step 3: Cross multiply
    7,778x = 10,209 × 10,209
  4. Step 4: Simplify right side
    7,778x = 104,223,681
  5. Step 5: Solve for x
    x = 104,223,681/7,778
  6. Step 6: Final answer
    x = 13,399.80

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.