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Finding the Third Proportional to 7,724 and 16,842

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Solution

The third proportional to 7,724 and 16,842 is: 36,723.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,724 : 16,842 = 16,842 : x
  2. Step 2: Convert to fraction form
    7,724/16,842 = 16,842/x
  3. Step 3: Cross multiply
    7,724x = 16,842 × 16,842
  4. Step 4: Simplify right side
    7,724x = 283,652,964
  5. Step 5: Solve for x
    x = 283,652,964/7,724
  6. Step 6: Final answer
    x = 36,723.58

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.