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Finding the Fourth Proportional to 1,109.47, 1,664.49 and 416.14

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Solution

The fourth proportional to 1,109.47, 1,664.49 and 416.14 is: 624.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,109.47 : 1,664.49 = 416.14 : x
  2. Step 2: Convert to fraction form
    1,109.47/1,664.49 = 416.14/x
  3. Step 3: Cross multiply
    1,109.47x = 1,664.49 × 416.14
  4. Step 4: Simplify right side
    1,109.47x = 692,658.79
  5. Step 5: Solve for x
    x = 692,658.79/1,109.47
  6. Step 6: Final answer
    x = 624.32

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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.