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Finding the Third Proportional to 7,776 and 10,206

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Solution

The third proportional to 7,776 and 10,206 is: 13,395.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,776 : 10,206 = 10,206 : x
  2. Step 2: Convert to fraction form
    7,776/10,206 = 10,206/x
  3. Step 3: Cross multiply
    7,776x = 10,206 × 10,206
  4. Step 4: Simplify right side
    7,776x = 104,162,436
  5. Step 5: Solve for x
    x = 104,162,436/7,776
  6. Step 6: Final answer
    x = 13,395.38

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.