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Finding the Third Proportional to 296,311 and 470,711

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Solution

The third proportional to 296,311 and 470,711 is: 747,757.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    296,311 : 470,711 = 470,711 : x
  2. Step 2: Convert to fraction form
    296,311/470,711 = 470,711/x
  3. Step 3: Cross multiply
    296,311x = 470,711 × 470,711
  4. Step 4: Simplify right side
    296,311x = 221,568,845,521
  5. Step 5: Solve for x
    x = 221,568,845,521/296,311
  6. Step 6: Final answer
    x = 747,757.75

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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.