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Finding the Fourth Proportional to 1,106.69, 1,660.78 and 457.42

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Solution

The fourth proportional to 1,106.69, 1,660.78 and 457.42 is: 686.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.69 : 1,660.78 = 457.42 : x
  2. Step 2: Convert to fraction form
    1,106.69/1,660.78 = 457.42/x
  3. Step 3: Cross multiply
    1,106.69x = 1,660.78 × 457.42
  4. Step 4: Simplify right side
    1,106.69x = 759,665.68
  5. Step 5: Solve for x
    x = 759,665.68/1,106.69
  6. Step 6: Final answer
    x = 686.43

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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.