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Finding the Fourth Proportional to 1,406.47, 2,109.69 and 419.29

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Solution

The fourth proportional to 1,406.47, 2,109.69 and 419.29 is: 628.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.47 : 2,109.69 = 419.29 : x
  2. Step 2: Convert to fraction form
    1,406.47/2,109.69 = 419.29/x
  3. Step 3: Cross multiply
    1,406.47x = 2,109.69 × 419.29
  4. Step 4: Simplify right side
    1,406.47x = 884,568.22
  5. Step 5: Solve for x
    x = 884,568.22/1,406.47
  6. Step 6: Final answer
    x = 628.93

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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.