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Finding the Third Proportional to 784 and 1,406

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Solution

The third proportional to 784 and 1,406 is: 2,521.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    784 : 1,406 = 1,406 : x
  2. Step 2: Convert to fraction form
    784/1,406 = 1,406/x
  3. Step 3: Cross multiply
    784x = 1,406 × 1,406
  4. Step 4: Simplify right side
    784x = 1,976,836
  5. Step 5: Solve for x
    x = 1,976,836/784
  6. Step 6: Final answer
    x = 2,521.47

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Why These Related Problems?

These problems maintain the same ratio (1.79) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.