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Finding the Third Proportional to 429.68 and 646.42

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Solution

The third proportional to 429.68 and 646.42 is: 972.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    429.68 : 646.42 = 646.42 : x
  2. Step 2: Convert to fraction form
    429.68/646.42 = 646.42/x
  3. Step 3: Cross multiply
    429.68x = 646.42 × 646.42
  4. Step 4: Simplify right side
    429.68x = 417,856.19
  5. Step 5: Solve for x
    x = 417,856.19/429.68
  6. Step 6: Final answer
    x = 972.48

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.