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Finding the Third Proportional to 12,312 and 19,804

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Solution

The third proportional to 12,312 and 19,804 is: 31,854.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,312 : 19,804 = 19,804 : x
  2. Step 2: Convert to fraction form
    12,312/19,804 = 19,804/x
  3. Step 3: Cross multiply
    12,312x = 19,804 × 19,804
  4. Step 4: Simplify right side
    12,312x = 392,198,416
  5. Step 5: Solve for x
    x = 392,198,416/12,312
  6. Step 6: Final answer
    x = 31,854.97

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.