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Finding the Third Proportional to 10,574 and 22,971

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Solution

The third proportional to 10,574 and 22,971 is: 49,902.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,574 : 22,971 = 22,971 : x
  2. Step 2: Convert to fraction form
    10,574/22,971 = 22,971/x
  3. Step 3: Cross multiply
    10,574x = 22,971 × 22,971
  4. Step 4: Simplify right side
    10,574x = 527,666,841
  5. Step 5: Solve for x
    x = 527,666,841/10,574
  6. Step 6: Final answer
    x = 49,902.29

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.