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Finding the Third Proportional to 1,709 and 2,838

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Solution

The third proportional to 1,709 and 2,838 is: 4,712.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,709 : 2,838 = 2,838 : x
  2. Step 2: Convert to fraction form
    1,709/2,838 = 2,838/x
  3. Step 3: Cross multiply
    1,709x = 2,838 × 2,838
  4. Step 4: Simplify right side
    1,709x = 8,054,244
  5. Step 5: Solve for x
    x = 8,054,244/1,709
  6. Step 6: Final answer
    x = 4,712.84

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.