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Finding the Third Proportional to 6,784 and 7,776

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Solution

The third proportional to 6,784 and 7,776 is: 8,913.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,784 : 7,776 = 7,776 : x
  2. Step 2: Convert to fraction form
    6,784/7,776 = 7,776/x
  3. Step 3: Cross multiply
    6,784x = 7,776 × 7,776
  4. Step 4: Simplify right side
    6,784x = 60,466,176
  5. Step 5: Solve for x
    x = 60,466,176/6,784
  6. Step 6: Final answer
    x = 8,913.06

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.