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Finding the Third Proportional to 856 and 2,306

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Solution

The third proportional to 856 and 2,306 is: 6,212.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    856 : 2,306 = 2,306 : x
  2. Step 2: Convert to fraction form
    856/2,306 = 2,306/x
  3. Step 3: Cross multiply
    856x = 2,306 × 2,306
  4. Step 4: Simplify right side
    856x = 5,317,636
  5. Step 5: Solve for x
    x = 5,317,636/856
  6. Step 6: Final answer
    x = 6,212.19

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Why These Related Problems?

These problems maintain the same ratio (2.69) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.