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Finding the Third Proportional to 784 and 1,656

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Solution

The third proportional to 784 and 1,656 is: 3,497.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    784 : 1,656 = 1,656 : x
  2. Step 2: Convert to fraction form
    784/1,656 = 1,656/x
  3. Step 3: Cross multiply
    784x = 1,656 × 1,656
  4. Step 4: Simplify right side
    784x = 2,742,336
  5. Step 5: Solve for x
    x = 2,742,336/784
  6. Step 6: Final answer
    x = 3,497.88

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.