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Finding the Third Proportional to 2,164 and 2,470

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Solution

The third proportional to 2,164 and 2,470 is: 2,819.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,164 : 2,470 = 2,470 : x
  2. Step 2: Convert to fraction form
    2,164/2,470 = 2,470/x
  3. Step 3: Cross multiply
    2,164x = 2,470 × 2,470
  4. Step 4: Simplify right side
    2,164x = 6,100,900
  5. Step 5: Solve for x
    x = 6,100,900/2,164
  6. Step 6: Final answer
    x = 2,819.27

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.