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Finding the Third Proportional to 429.75 and 709.13

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Solution

The third proportional to 429.75 and 709.13 is: 1,170.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    429.75 : 709.13 = 709.13 : x
  2. Step 2: Convert to fraction form
    429.75/709.13 = 709.13/x
  3. Step 3: Cross multiply
    429.75x = 709.13 × 709.13
  4. Step 4: Simplify right side
    429.75x = 502,858.27
  5. Step 5: Solve for x
    x = 502,858.27/429.75
  6. Step 6: Final answer
    x = 1,170.12

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.