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Finding the Third Proportional to 177.50 and 289.25

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Solution

The third proportional to 177.50 and 289.25 is: 471.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    177.50 : 289.25 = 289.25 : x
  2. Step 2: Convert to fraction form
    177.50/289.25 = 289.25/x
  3. Step 3: Cross multiply
    177.50x = 289.25 × 289.25
  4. Step 4: Simplify right side
    177.50x = 83,665.56
  5. Step 5: Solve for x
    x = 83,665.56/177.50
  6. Step 6: Final answer
    x = 471.36

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.