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Finding the Third Proportional to 2,409 and 5,202

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Solution

The third proportional to 2,409 and 5,202 is: 11,233.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,409 : 5,202 = 5,202 : x
  2. Step 2: Convert to fraction form
    2,409/5,202 = 5,202/x
  3. Step 3: Cross multiply
    2,409x = 5,202 × 5,202
  4. Step 4: Simplify right side
    2,409x = 27,060,804
  5. Step 5: Solve for x
    x = 27,060,804/2,409
  6. Step 6: Final answer
    x = 11,233.21

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.