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Finding the Third Proportional to 14,512 and 31,814

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Solution

The third proportional to 14,512 and 31,814 is: 69,744.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,512 : 31,814 = 31,814 : x
  2. Step 2: Convert to fraction form
    14,512/31,814 = 31,814/x
  3. Step 3: Cross multiply
    14,512x = 31,814 × 31,814
  4. Step 4: Simplify right side
    14,512x = 1,012,130,596
  5. Step 5: Solve for x
    x = 1,012,130,596/14,512
  6. Step 6: Final answer
    x = 69,744.39

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.