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Finding the Third Proportional to 6,500 and 7,112

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Solution

The third proportional to 6,500 and 7,112 is: 7,781.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,500 : 7,112 = 7,112 : x
  2. Step 2: Convert to fraction form
    6,500/7,112 = 7,112/x
  3. Step 3: Cross multiply
    6,500x = 7,112 × 7,112
  4. Step 4: Simplify right side
    6,500x = 50,580,544
  5. Step 5: Solve for x
    x = 50,580,544/6,500
  6. Step 6: Final answer
    x = 7,781.62

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.