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Finding the Third Proportional to 411.75 and 473.06

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Solution

The third proportional to 411.75 and 473.06 is: 543.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    411.75 : 473.06 = 473.06 : x
  2. Step 2: Convert to fraction form
    411.75/473.06 = 473.06/x
  3. Step 3: Cross multiply
    411.75x = 473.06 × 473.06
  4. Step 4: Simplify right side
    411.75x = 223,788.13
  5. Step 5: Solve for x
    x = 223,788.13/411.75
  6. Step 6: Final answer
    x = 543.50

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.