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Finding the Third Proportional to 257,700 and 409,974

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Solution

The third proportional to 257,700 and 409,974 is: 652,226.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,700 : 409,974 = 409,974 : x
  2. Step 2: Convert to fraction form
    257,700/409,974 = 409,974/x
  3. Step 3: Cross multiply
    257,700x = 409,974 × 409,974
  4. Step 4: Simplify right side
    257,700x = 168,078,680,676
  5. Step 5: Solve for x
    x = 168,078,680,676/257,700
  6. Step 6: Final answer
    x = 652,226.16

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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.