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Finding the Third Proportional to 415.76 and 646.42

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Solution

The third proportional to 415.76 and 646.42 is: 1,005.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.76 : 646.42 = 646.42 : x
  2. Step 2: Convert to fraction form
    415.76/646.42 = 646.42/x
  3. Step 3: Cross multiply
    415.76x = 646.42 × 646.42
  4. Step 4: Simplify right side
    415.76x = 417,856.19
  5. Step 5: Solve for x
    x = 417,856.19/415.76
  6. Step 6: Final answer
    x = 1,005.05

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.