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Finding the Fourth Proportional to 1,106.61, 1,659.78 and 457.14

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Solution

The fourth proportional to 1,106.61, 1,659.78 and 457.14 is: 685.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.61 : 1,659.78 = 457.14 : x
  2. Step 2: Convert to fraction form
    1,106.61/1,659.78 = 457.14/x
  3. Step 3: Cross multiply
    1,106.61x = 1,659.78 × 457.14
  4. Step 4: Simplify right side
    1,106.61x = 758,751.83
  5. Step 5: Solve for x
    x = 758,751.83/1,106.61
  6. Step 6: Final answer
    x = 685.65

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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.