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Finding the Third Proportional to 311,898 and 470,946

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Solution

The third proportional to 311,898 and 470,946 is: 711,098.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    311,898 : 470,946 = 470,946 : x
  2. Step 2: Convert to fraction form
    311,898/470,946 = 470,946/x
  3. Step 3: Cross multiply
    311,898x = 470,946 × 470,946
  4. Step 4: Simplify right side
    311,898x = 221,790,134,916
  5. Step 5: Solve for x
    x = 221,790,134,916/311,898
  6. Step 6: Final answer
    x = 711,098.29

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.