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Finding the Third Proportional to 5,202 and 7,411

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Solution

The third proportional to 5,202 and 7,411 is: 10,558.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,202 : 7,411 = 7,411 : x
  2. Step 2: Convert to fraction form
    5,202/7,411 = 7,411/x
  3. Step 3: Cross multiply
    5,202x = 7,411 × 7,411
  4. Step 4: Simplify right side
    5,202x = 54,922,921
  5. Step 5: Solve for x
    x = 54,922,921/5,202
  6. Step 6: Final answer
    x = 10,558.04

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.