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Finding the Third Proportional to 406 and 471.50

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Solution

The third proportional to 406 and 471.50 is: 547.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    406 : 471.50 = 471.50 : x
  2. Step 2: Convert to fraction form
    406/471.50 = 471.50/x
  3. Step 3: Cross multiply
    406x = 471.50 × 471.50
  4. Step 4: Simplify right side
    406x = 222,312.25
  5. Step 5: Solve for x
    x = 222,312.25/406
  6. Step 6: Final answer
    x = 547.57

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.