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Finding the Fourth Proportional to 728.84, 1,005.76 and 414.06

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Solution

The fourth proportional to 728.84, 1,005.76 and 414.06 is: 571.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    728.84 : 1,005.76 = 414.06 : x
  2. Step 2: Convert to fraction form
    728.84/1,005.76 = 414.06/x
  3. Step 3: Cross multiply
    728.84x = 1,005.76 × 414.06
  4. Step 4: Simplify right side
    728.84x = 416,444.99
  5. Step 5: Solve for x
    x = 416,444.99/728.84
  6. Step 6: Final answer
    x = 571.38

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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.