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Finding the Third Proportional to 784 and 1,209

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Solution

The third proportional to 784 and 1,209 is: 1,864.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    784 : 1,209 = 1,209 : x
  2. Step 2: Convert to fraction form
    784/1,209 = 1,209/x
  3. Step 3: Cross multiply
    784x = 1,209 × 1,209
  4. Step 4: Simplify right side
    784x = 1,461,681
  5. Step 5: Solve for x
    x = 1,461,681/784
  6. Step 6: Final answer
    x = 1,864.39

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.