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Finding the Third Proportional to 24,084 and 31,964

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Solution

The third proportional to 24,084 and 31,964 is: 42,422.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    24,084 : 31,964 = 31,964 : x
  2. Step 2: Convert to fraction form
    24,084/31,964 = 31,964/x
  3. Step 3: Cross multiply
    24,084x = 31,964 × 31,964
  4. Step 4: Simplify right side
    24,084x = 1,021,697,296
  5. Step 5: Solve for x
    x = 1,021,697,296/24,084
  6. Step 6: Final answer
    x = 42,422.24

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.