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Finding the Fourth Proportional to 829, 1,242.92 and 412.24

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Solution

The fourth proportional to 829, 1,242.92 and 412.24 is: 618.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,242.92 = 412.24 : x
  2. Step 2: Convert to fraction form
    829/1,242.92 = 412.24/x
  3. Step 3: Cross multiply
    829x = 1,242.92 × 412.24
  4. Step 4: Simplify right side
    829x = 512,381.34
  5. Step 5: Solve for x
    x = 512,381.34/829
  6. Step 6: Final answer
    x = 618.07

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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.