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Finding the Third Proportional to 7,762 and 10,265

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Solution

The third proportional to 7,762 and 10,265 is: 13,575.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,762 : 10,265 = 10,265 : x
  2. Step 2: Convert to fraction form
    7,762/10,265 = 10,265/x
  3. Step 3: Cross multiply
    7,762x = 10,265 × 10,265
  4. Step 4: Simplify right side
    7,762x = 105,370,225
  5. Step 5: Solve for x
    x = 105,370,225/7,762
  6. Step 6: Final answer
    x = 13,575.14

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.