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Finding the Third Proportional to 102,023 and 218,789

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Solution

The third proportional to 102,023 and 218,789 is: 469,194.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,023 : 218,789 = 218,789 : x
  2. Step 2: Convert to fraction form
    102,023/218,789 = 218,789/x
  3. Step 3: Cross multiply
    102,023x = 218,789 × 218,789
  4. Step 4: Simplify right side
    102,023x = 47,868,626,521
  5. Step 5: Solve for x
    x = 47,868,626,521/102,023
  6. Step 6: Final answer
    x = 469,194.46

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.