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Finding the Third Proportional to 2,184 and 2,834

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Solution

The third proportional to 2,184 and 2,834 is: 3,677.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,184 : 2,834 = 2,834 : x
  2. Step 2: Convert to fraction form
    2,184/2,834 = 2,834/x
  3. Step 3: Cross multiply
    2,184x = 2,834 × 2,834
  4. Step 4: Simplify right side
    2,184x = 8,031,556
  5. Step 5: Solve for x
    x = 8,031,556/2,184
  6. Step 6: Final answer
    x = 3,677.45

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.