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Finding the Third Proportional to 7,697 and 17,657

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Solution

The third proportional to 7,697 and 17,657 is: 40,505.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,697 : 17,657 = 17,657 : x
  2. Step 2: Convert to fraction form
    7,697/17,657 = 17,657/x
  3. Step 3: Cross multiply
    7,697x = 17,657 × 17,657
  4. Step 4: Simplify right side
    7,697x = 311,769,649
  5. Step 5: Solve for x
    x = 311,769,649/7,697
  6. Step 6: Final answer
    x = 40,505.35

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Why These Related Problems?

These problems maintain the same ratio (2.29) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.