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Finding the Fourth Proportional to 31,782.84, 47,676.54 and 8,409

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Solution

The fourth proportional to 31,782.84, 47,676.54 and 8,409 is: 12,614.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,782.84 : 47,676.54 = 8,409 : x
  2. Step 2: Convert to fraction form
    31,782.84/47,676.54 = 8,409/x
  3. Step 3: Cross multiply
    31,782.84x = 47,676.54 × 8,409
  4. Step 4: Simplify right side
    31,782.84x = 400,912,024.86
  5. Step 5: Solve for x
    x = 400,912,024.86/31,782.84
  6. Step 6: Final answer
    x = 12,614.10

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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.