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Finding the Third Proportional to 5,724 and 8,416

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Solution

The third proportional to 5,724 and 8,416 is: 12,374.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,724 : 8,416 = 8,416 : x
  2. Step 2: Convert to fraction form
    5,724/8,416 = 8,416/x
  3. Step 3: Cross multiply
    5,724x = 8,416 × 8,416
  4. Step 4: Simplify right side
    5,724x = 70,829,056
  5. Step 5: Solve for x
    x = 70,829,056/5,724
  6. Step 6: Final answer
    x = 12,374.05

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.