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Finding the Third Proportional to 6,820 and 7,780

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Solution

The third proportional to 6,820 and 7,780 is: 8,875.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,820 : 7,780 = 7,780 : x
  2. Step 2: Convert to fraction form
    6,820/7,780 = 7,780/x
  3. Step 3: Cross multiply
    6,820x = 7,780 × 7,780
  4. Step 4: Simplify right side
    6,820x = 60,528,400
  5. Step 5: Solve for x
    x = 60,528,400/6,820
  6. Step 6: Final answer
    x = 8,875.13

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.