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Finding the Fourth Proportional to 1,029.75, 1,543.69 and 509.43

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Solution

The fourth proportional to 1,029.75, 1,543.69 and 509.43 is: 763.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,029.75 : 1,543.69 = 509.43 : x
  2. Step 2: Convert to fraction form
    1,029.75/1,543.69 = 509.43/x
  3. Step 3: Cross multiply
    1,029.75x = 1,543.69 × 509.43
  4. Step 4: Simplify right side
    1,029.75x = 786,402.00
  5. Step 5: Solve for x
    x = 786,402.00/1,029.75
  6. Step 6: Final answer
    x = 763.68

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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.