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Finding the Third Proportional to 7,785 and 10,219

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Solution

The third proportional to 7,785 and 10,219 is: 13,414.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,785 : 10,219 = 10,219 : x
  2. Step 2: Convert to fraction form
    7,785/10,219 = 10,219/x
  3. Step 3: Cross multiply
    7,785x = 10,219 × 10,219
  4. Step 4: Simplify right side
    7,785x = 104,427,961
  5. Step 5: Solve for x
    x = 104,427,961/7,785
  6. Step 6: Final answer
    x = 13,414.00

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.