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Finding the Third Proportional to 784 and 1,648

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Solution

The third proportional to 784 and 1,648 is: 3,464.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    784 : 1,648 = 1,648 : x
  2. Step 2: Convert to fraction form
    784/1,648 = 1,648/x
  3. Step 3: Cross multiply
    784x = 1,648 × 1,648
  4. Step 4: Simplify right side
    784x = 2,715,904
  5. Step 5: Solve for x
    x = 2,715,904/784
  6. Step 6: Final answer
    x = 3,464.16

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.