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Finding the Third Proportional to 1,309 and 2,834

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Solution

The third proportional to 1,309 and 2,834 is: 6,135.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,309 : 2,834 = 2,834 : x
  2. Step 2: Convert to fraction form
    1,309/2,834 = 2,834/x
  3. Step 3: Cross multiply
    1,309x = 2,834 × 2,834
  4. Step 4: Simplify right side
    1,309x = 8,031,556
  5. Step 5: Solve for x
    x = 8,031,556/1,309
  6. Step 6: Final answer
    x = 6,135.64

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.