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Finding the Third Proportional to 2,164 and 2,371

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Solution

The third proportional to 2,164 and 2,371 is: 2,597.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,164 : 2,371 = 2,371 : x
  2. Step 2: Convert to fraction form
    2,164/2,371 = 2,371/x
  3. Step 3: Cross multiply
    2,164x = 2,371 × 2,371
  4. Step 4: Simplify right side
    2,164x = 5,621,641
  5. Step 5: Solve for x
    x = 5,621,641/2,164
  6. Step 6: Final answer
    x = 2,597.80

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.