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Finding the Third Proportional to 4,210 and 6,411

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Solution

The third proportional to 4,210 and 6,411 is: 9,762.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,210 : 6,411 = 6,411 : x
  2. Step 2: Convert to fraction form
    4,210/6,411 = 6,411/x
  3. Step 3: Cross multiply
    4,210x = 6,411 × 6,411
  4. Step 4: Simplify right side
    4,210x = 41,100,921
  5. Step 5: Solve for x
    x = 41,100,921/4,210
  6. Step 6: Final answer
    x = 9,762.69

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.