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Finding the Fourth Proportional to 1,106.64, 1,660.14 and 457.83

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Solution

The fourth proportional to 1,106.64, 1,660.14 and 457.83 is: 686.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.64 : 1,660.14 = 457.83 : x
  2. Step 2: Convert to fraction form
    1,106.64/1,660.14 = 457.83/x
  3. Step 3: Cross multiply
    1,106.64x = 1,660.14 × 457.83
  4. Step 4: Simplify right side
    1,106.64x = 760,061.90
  5. Step 5: Solve for x
    x = 760,061.90/1,106.64
  6. Step 6: Final answer
    x = 686.82

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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.