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Finding the Fourth Proportional to 1,406.40, 2,109.56 and 584.16

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Solution

The fourth proportional to 1,406.40, 2,109.56 and 584.16 is: 876.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.40 : 2,109.56 = 584.16 : x
  2. Step 2: Convert to fraction form
    1,406.40/2,109.56 = 584.16/x
  3. Step 3: Cross multiply
    1,406.40x = 2,109.56 × 584.16
  4. Step 4: Simplify right side
    1,406.40x = 1,232,320.57
  5. Step 5: Solve for x
    x = 1,232,320.57/1,406.40
  6. Step 6: Final answer
    x = 876.22

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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.