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Finding the Third Proportional to 784 and 1,909

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Solution

The third proportional to 784 and 1,909 is: 4,648.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    784 : 1,909 = 1,909 : x
  2. Step 2: Convert to fraction form
    784/1,909 = 1,909/x
  3. Step 3: Cross multiply
    784x = 1,909 × 1,909
  4. Step 4: Simplify right side
    784x = 3,644,281
  5. Step 5: Solve for x
    x = 3,644,281/784
  6. Step 6: Final answer
    x = 4,648.32

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.