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Finding the Fourth Proportional to 457.70, 686.10 and 409.10

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Solution

The fourth proportional to 457.70, 686.10 and 409.10 is: 613.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    457.70 : 686.10 = 409.10 : x
  2. Step 2: Convert to fraction form
    457.70/686.10 = 409.10/x
  3. Step 3: Cross multiply
    457.70x = 686.10 × 409.10
  4. Step 4: Simplify right side
    457.70x = 280,683.51
  5. Step 5: Solve for x
    x = 280,683.51/457.70
  6. Step 6: Final answer
    x = 613.25

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.