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Finding the Fourth Proportional to 829, 1,143.96 and 509.86

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Solution

The fourth proportional to 829, 1,143.96 and 509.86 is: 703.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    829 : 1,143.96 = 509.86 : x
  2. Step 2: Convert to fraction form
    829/1,143.96 = 509.86/x
  3. Step 3: Cross multiply
    829x = 1,143.96 × 509.86
  4. Step 4: Simplify right side
    829x = 583,259.45
  5. Step 5: Solve for x
    x = 583,259.45/829
  6. Step 6: Final answer
    x = 703.57

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.