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Finding the Third Proportional to 784 and 1,378

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Solution

The third proportional to 784 and 1,378 is: 2,422.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    784 : 1,378 = 1,378 : x
  2. Step 2: Convert to fraction form
    784/1,378 = 1,378/x
  3. Step 3: Cross multiply
    784x = 1,378 × 1,378
  4. Step 4: Simplify right side
    784x = 1,898,884
  5. Step 5: Solve for x
    x = 1,898,884/784
  6. Step 6: Final answer
    x = 2,422.05

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Why These Related Problems?

These problems maintain the same ratio (1.76) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.