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Finding the Third Proportional to 7,730 and 8,546

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Solution

The third proportional to 7,730 and 8,546 is: 9,448.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,730 : 8,546 = 8,546 : x
  2. Step 2: Convert to fraction form
    7,730/8,546 = 8,546/x
  3. Step 3: Cross multiply
    7,730x = 8,546 × 8,546
  4. Step 4: Simplify right side
    7,730x = 73,034,116
  5. Step 5: Solve for x
    x = 73,034,116/7,730
  6. Step 6: Final answer
    x = 9,448.14

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.