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Finding the Third Proportional to 7,786 and 8,578

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Solution

The third proportional to 7,786 and 8,578 is: 9,450.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,786 : 8,578 = 8,578 : x
  2. Step 2: Convert to fraction form
    7,786/8,578 = 8,578/x
  3. Step 3: Cross multiply
    7,786x = 8,578 × 8,578
  4. Step 4: Simplify right side
    7,786x = 73,582,084
  5. Step 5: Solve for x
    x = 73,582,084/7,786
  6. Step 6: Final answer
    x = 9,450.56

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.