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Finding the Third Proportional to 7,830 and 9,454

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Solution

The third proportional to 7,830 and 9,454 is: 11,414.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,830 : 9,454 = 9,454 : x
  2. Step 2: Convert to fraction form
    7,830/9,454 = 9,454/x
  3. Step 3: Cross multiply
    7,830x = 9,454 × 9,454
  4. Step 4: Simplify right side
    7,830x = 89,378,116
  5. Step 5: Solve for x
    x = 89,378,116/7,830
  6. Step 6: Final answer
    x = 11,414.83

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.