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Finding the Fourth Proportional to 1,106.57, 1,659.72 and 456.95

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Solution

The fourth proportional to 1,106.57, 1,659.72 and 456.95 is: 685.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106.57 : 1,659.72 = 456.95 : x
  2. Step 2: Convert to fraction form
    1,106.57/1,659.72 = 456.95/x
  3. Step 3: Cross multiply
    1,106.57x = 1,659.72 × 456.95
  4. Step 4: Simplify right side
    1,106.57x = 758,409.05
  5. Step 5: Solve for x
    x = 758,409.05/1,106.57
  6. Step 6: Final answer
    x = 685.37

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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.