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Finding the Third Proportional to 419.13 and 653.97

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Solution

The third proportional to 419.13 and 653.97 is: 1,020.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.13 : 653.97 = 653.97 : x
  2. Step 2: Convert to fraction form
    419.13/653.97 = 653.97/x
  3. Step 3: Cross multiply
    419.13x = 653.97 × 653.97
  4. Step 4: Simplify right side
    419.13x = 427,675.13
  5. Step 5: Solve for x
    x = 427,675.13/419.13
  6. Step 6: Final answer
    x = 1,020.40

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.