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Finding the Third Proportional to 312,972 and 470,956

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Solution

The third proportional to 312,972 and 470,956 is: 708,688.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    312,972 : 470,956 = 470,956 : x
  2. Step 2: Convert to fraction form
    312,972/470,956 = 470,956/x
  3. Step 3: Cross multiply
    312,972x = 470,956 × 470,956
  4. Step 4: Simplify right side
    312,972x = 221,799,553,936
  5. Step 5: Solve for x
    x = 221,799,553,936/312,972
  6. Step 6: Final answer
    x = 708,688.17

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.