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Finding the Third Proportional to 257,218 and 564,237

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Solution

The third proportional to 257,218 and 564,237 is: 1,237,718.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,218 : 564,237 = 564,237 : x
  2. Step 2: Convert to fraction form
    257,218/564,237 = 564,237/x
  3. Step 3: Cross multiply
    257,218x = 564,237 × 564,237
  4. Step 4: Simplify right side
    257,218x = 318,363,392,169
  5. Step 5: Solve for x
    x = 318,363,392,169/257,218
  6. Step 6: Final answer
    x = 1,237,718.17

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.