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Finding the Third Proportional to 420.75 and 659.25

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Solution

The third proportional to 420.75 and 659.25 is: 1,032.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.75 : 659.25 = 659.25 : x
  2. Step 2: Convert to fraction form
    420.75/659.25 = 659.25/x
  3. Step 3: Cross multiply
    420.75x = 659.25 × 659.25
  4. Step 4: Simplify right side
    420.75x = 434,610.56
  5. Step 5: Solve for x
    x = 434,610.56/420.75
  6. Step 6: Final answer
    x = 1,032.94

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.