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Finding the Third Proportional to 7,724 and 8,516

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Solution

The third proportional to 7,724 and 8,516 is: 9,389.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,724 : 8,516 = 8,516 : x
  2. Step 2: Convert to fraction form
    7,724/8,516 = 8,516/x
  3. Step 3: Cross multiply
    7,724x = 8,516 × 8,516
  4. Step 4: Simplify right side
    7,724x = 72,522,256
  5. Step 5: Solve for x
    x = 72,522,256/7,724
  6. Step 6: Final answer
    x = 9,389.21

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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.