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Finding the Third Proportional to 78,224 and 106,278

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Solution

The third proportional to 78,224 and 106,278 is: 144,393.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    78,224 : 106,278 = 106,278 : x
  2. Step 2: Convert to fraction form
    78,224/106,278 = 106,278/x
  3. Step 3: Cross multiply
    78,224x = 106,278 × 106,278
  4. Step 4: Simplify right side
    78,224x = 11,295,013,284
  5. Step 5: Solve for x
    x = 11,295,013,284/78,224
  6. Step 6: Final answer
    x = 144,393.19

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.