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Finding the Third Proportional to 2,416 and 4,114

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Solution

The third proportional to 2,416 and 4,114 is: 7,005.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,416 : 4,114 = 4,114 : x
  2. Step 2: Convert to fraction form
    2,416/4,114 = 4,114/x
  3. Step 3: Cross multiply
    2,416x = 4,114 × 4,114
  4. Step 4: Simplify right side
    2,416x = 16,924,996
  5. Step 5: Solve for x
    x = 16,924,996/2,416
  6. Step 6: Final answer
    x = 7,005.38

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Why These Related Problems?

These problems maintain the same ratio (1.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.