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Finding the Third Proportional to 12,584 and 19,754

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Solution

The third proportional to 12,584 and 19,754 is: 31,009.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,584 : 19,754 = 19,754 : x
  2. Step 2: Convert to fraction form
    12,584/19,754 = 19,754/x
  3. Step 3: Cross multiply
    12,584x = 19,754 × 19,754
  4. Step 4: Simplify right side
    12,584x = 390,220,516
  5. Step 5: Solve for x
    x = 390,220,516/12,584
  6. Step 6: Final answer
    x = 31,009.26

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.