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Finding the Third Proportional to 4,213 and 4,663

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Solution

The third proportional to 4,213 and 4,663 is: 5,161.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,213 : 4,663 = 4,663 : x
  2. Step 2: Convert to fraction form
    4,213/4,663 = 4,663/x
  3. Step 3: Cross multiply
    4,213x = 4,663 × 4,663
  4. Step 4: Simplify right side
    4,213x = 21,743,569
  5. Step 5: Solve for x
    x = 21,743,569/4,213
  6. Step 6: Final answer
    x = 5,161.07

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.