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Finding the Third Proportional to 7,780 and 10,506

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Solution

The third proportional to 7,780 and 10,506 is: 14,187.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,780 : 10,506 = 10,506 : x
  2. Step 2: Convert to fraction form
    7,780/10,506 = 10,506/x
  3. Step 3: Cross multiply
    7,780x = 10,506 × 10,506
  4. Step 4: Simplify right side
    7,780x = 110,376,036
  5. Step 5: Solve for x
    x = 110,376,036/7,780
  6. Step 6: Final answer
    x = 14,187.15

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.