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Finding the Fourth Proportional to 1,029.78, 1,543.86 and 509.22

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Solution

The fourth proportional to 1,029.78, 1,543.86 and 509.22 is: 763.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029.78 : 1,543.86 = 509.22 : x
  2. Step 2: Convert to fraction form
    1,029.78/1,543.86 = 509.22/x
  3. Step 3: Cross multiply
    1,029.78x = 1,543.86 × 509.22
  4. Step 4: Simplify right side
    1,029.78x = 786,164.39
  5. Step 5: Solve for x
    x = 786,164.39/1,029.78
  6. Step 6: Final answer
    x = 763.43

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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.