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Finding the Third Proportional to 2,114 and 2,306

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Solution

The third proportional to 2,114 and 2,306 is: 2,515.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,114 : 2,306 = 2,306 : x
  2. Step 2: Convert to fraction form
    2,114/2,306 = 2,306/x
  3. Step 3: Cross multiply
    2,114x = 2,306 × 2,306
  4. Step 4: Simplify right side
    2,114x = 5,317,636
  5. Step 5: Solve for x
    x = 5,317,636/2,114
  6. Step 6: Final answer
    x = 2,515.44

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.