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Finding the Third Proportional to 402,720 and 564,416

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Solution

The third proportional to 402,720 and 564,416 is: 791,034.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    402,720 : 564,416 = 564,416 : x
  2. Step 2: Convert to fraction form
    402,720/564,416 = 564,416/x
  3. Step 3: Cross multiply
    402,720x = 564,416 × 564,416
  4. Step 4: Simplify right side
    402,720x = 318,565,421,056
  5. Step 5: Solve for x
    x = 318,565,421,056/402,720
  6. Step 6: Final answer
    x = 791,034.52

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.