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Finding the Third Proportional to 7,830 and 9,103.50

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Solution

The third proportional to 7,830 and 9,103.50 is: 10,584.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,830 : 9,103.50 = 9,103.50 : x
  2. Step 2: Convert to fraction form
    7,830/9,103.50 = 9,103.50/x
  3. Step 3: Cross multiply
    7,830x = 9,103.50 × 9,103.50
  4. Step 4: Simplify right side
    7,830x = 82,873,712.25
  5. Step 5: Solve for x
    x = 82,873,712.25/7,830
  6. Step 6: Final answer
    x = 10,584.13

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.