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Finding the Fourth Proportional to 1,242.57, 1,864.14 and 409.70

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Solution

The fourth proportional to 1,242.57, 1,864.14 and 409.70 is: 614.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,242.57 : 1,864.14 = 409.70 : x
  2. Step 2: Convert to fraction form
    1,242.57/1,864.14 = 409.70/x
  3. Step 3: Cross multiply
    1,242.57x = 1,864.14 × 409.70
  4. Step 4: Simplify right side
    1,242.57x = 763,728.84
  5. Step 5: Solve for x
    x = 763,728.84/1,242.57
  6. Step 6: Final answer
    x = 614.64

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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.