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Finding the Fourth Proportional to 1,409, 2,112.86 and 542.68

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Solution

The fourth proportional to 1,409, 2,112.86 and 542.68 is: 813.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,409 : 2,112.86 = 542.68 : x
  2. Step 2: Convert to fraction form
    1,409/2,112.86 = 542.68/x
  3. Step 3: Cross multiply
    1,409x = 2,112.86 × 542.68
  4. Step 4: Simplify right side
    1,409x = 1,146,606.86
  5. Step 5: Solve for x
    x = 1,146,606.86/1,409
  6. Step 6: Final answer
    x = 813.77

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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.