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Finding the Third Proportional to 7,838 and 8,606

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Solution

The third proportional to 7,838 and 8,606 is: 9,449.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,838 : 8,606 = 8,606 : x
  2. Step 2: Convert to fraction form
    7,838/8,606 = 8,606/x
  3. Step 3: Cross multiply
    7,838x = 8,606 × 8,606
  4. Step 4: Simplify right side
    7,838x = 74,063,236
  5. Step 5: Solve for x
    x = 74,063,236/7,838
  6. Step 6: Final answer
    x = 9,449.25

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.