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Finding the Fourth Proportional to 1,406.61, 2,109.30 and 822.19

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Solution

The fourth proportional to 1,406.61, 2,109.30 and 822.19 is: 1,232.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.61 : 2,109.30 = 822.19 : x
  2. Step 2: Convert to fraction form
    1,406.61/2,109.30 = 822.19/x
  3. Step 3: Cross multiply
    1,406.61x = 2,109.30 × 822.19
  4. Step 4: Simplify right side
    1,406.61x = 1,734,245.37
  5. Step 5: Solve for x
    x = 1,734,245.37/1,406.61
  6. Step 6: Final answer
    x = 1,232.93

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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.