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Finding the Third Proportional to 1,709 and 4,106

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Solution

The third proportional to 1,709 and 4,106 is: 9,864.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,709 : 4,106 = 4,106 : x
  2. Step 2: Convert to fraction form
    1,709/4,106 = 4,106/x
  3. Step 3: Cross multiply
    1,709x = 4,106 × 4,106
  4. Step 4: Simplify right side
    1,709x = 16,859,236
  5. Step 5: Solve for x
    x = 16,859,236/1,709
  6. Step 6: Final answer
    x = 9,864.97

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Why These Related Problems?

These problems maintain the same ratio (2.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.