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Finding the Third Proportional to 6,478 and 9,712

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Solution

The third proportional to 6,478 and 9,712 is: 14,560.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,478 : 9,712 = 9,712 : x
  2. Step 2: Convert to fraction form
    6,478/9,712 = 9,712/x
  3. Step 3: Cross multiply
    6,478x = 9,712 × 9,712
  4. Step 4: Simplify right side
    6,478x = 94,322,944
  5. Step 5: Solve for x
    x = 94,322,944/6,478
  6. Step 6: Final answer
    x = 14,560.50

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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.