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Finding the Third Proportional to 6,180 and 7,854

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Solution

The third proportional to 6,180 and 7,854 is: 9,981.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,180 : 7,854 = 7,854 : x
  2. Step 2: Convert to fraction form
    6,180/7,854 = 7,854/x
  3. Step 3: Cross multiply
    6,180x = 7,854 × 7,854
  4. Step 4: Simplify right side
    6,180x = 61,685,316
  5. Step 5: Solve for x
    x = 61,685,316/6,180
  6. Step 6: Final answer
    x = 9,981.44

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.