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Finding the Third Proportional to 3,407 and 5,210

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Solution

The third proportional to 3,407 and 5,210 is: 7,967.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,407 : 5,210 = 5,210 : x
  2. Step 2: Convert to fraction form
    3,407/5,210 = 5,210/x
  3. Step 3: Cross multiply
    3,407x = 5,210 × 5,210
  4. Step 4: Simplify right side
    3,407x = 27,144,100
  5. Step 5: Solve for x
    x = 27,144,100/3,407
  6. Step 6: Final answer
    x = 7,967.16

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.