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Finding the Third Proportional to 257,210 and 564,223

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Solution

The third proportional to 257,210 and 564,223 is: 1,237,695.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,210 : 564,223 = 564,223 : x
  2. Step 2: Convert to fraction form
    257,210/564,223 = 564,223/x
  3. Step 3: Cross multiply
    257,210x = 564,223 × 564,223
  4. Step 4: Simplify right side
    257,210x = 318,347,593,729
  5. Step 5: Solve for x
    x = 318,347,593,729/257,210
  6. Step 6: Final answer
    x = 1,237,695.24

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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.