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Finding the Third Proportional to 420.75 and 653.91

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Solution

The third proportional to 420.75 and 653.91 is: 1,016.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.75 : 653.91 = 653.91 : x
  2. Step 2: Convert to fraction form
    420.75/653.91 = 653.91/x
  3. Step 3: Cross multiply
    420.75x = 653.91 × 653.91
  4. Step 4: Simplify right side
    420.75x = 427,593.38
  5. Step 5: Solve for x
    x = 427,593.38/420.75
  6. Step 6: Final answer
    x = 1,016.26

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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.