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Finding the Third Proportional to 10,024 and 15,724

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Solution

The third proportional to 10,024 and 15,724 is: 24,665.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,024 : 15,724 = 15,724 : x
  2. Step 2: Convert to fraction form
    10,024/15,724 = 15,724/x
  3. Step 3: Cross multiply
    10,024x = 15,724 × 15,724
  4. Step 4: Simplify right side
    10,024x = 247,244,176
  5. Step 5: Solve for x
    x = 247,244,176/10,024
  6. Step 6: Final answer
    x = 24,665.22

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.