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Finding the Fourth Proportional to 1,406.60, 2,109.40 and 419.12

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Solution

The fourth proportional to 1,406.60, 2,109.40 and 419.12 is: 628.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.60 : 2,109.40 = 419.12 : x
  2. Step 2: Convert to fraction form
    1,406.60/2,109.40 = 419.12/x
  3. Step 3: Cross multiply
    1,406.60x = 2,109.40 × 419.12
  4. Step 4: Simplify right side
    1,406.60x = 884,091.73
  5. Step 5: Solve for x
    x = 884,091.73/1,406.60
  6. Step 6: Final answer
    x = 628.53

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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.