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Finding the Third Proportional to 2,085 and 2,709

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Solution

The third proportional to 2,085 and 2,709 is: 3,519.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,085 : 2,709 = 2,709 : x
  2. Step 2: Convert to fraction form
    2,085/2,709 = 2,709/x
  3. Step 3: Cross multiply
    2,085x = 2,709 × 2,709
  4. Step 4: Simplify right side
    2,085x = 7,338,681
  5. Step 5: Solve for x
    x = 7,338,681/2,085
  6. Step 6: Final answer
    x = 3,519.75

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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.