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Finding the Third Proportional to 7,724 and 11,623

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Solution

The third proportional to 7,724 and 11,623 is: 17,490.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,724 : 11,623 = 11,623 : x
  2. Step 2: Convert to fraction form
    7,724/11,623 = 11,623/x
  3. Step 3: Cross multiply
    7,724x = 11,623 × 11,623
  4. Step 4: Simplify right side
    7,724x = 135,094,129
  5. Step 5: Solve for x
    x = 135,094,129/7,724
  6. Step 6: Final answer
    x = 17,490.18

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.