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Finding the Fourth Proportional to 497.50, 685.82 and 410.02

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Solution

The fourth proportional to 497.50, 685.82 and 410.02 is: 565.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    497.50 : 685.82 = 410.02 : x
  2. Step 2: Convert to fraction form
    497.50/685.82 = 410.02/x
  3. Step 3: Cross multiply
    497.50x = 685.82 × 410.02
  4. Step 4: Simplify right side
    497.50x = 281,199.92
  5. Step 5: Solve for x
    x = 281,199.92/497.50
  6. Step 6: Final answer
    x = 565.23

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.