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Finding the Third Proportional to 51,470 and 77,205

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Solution

The third proportional to 51,470 and 77,205 is: 115,807.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,470 : 77,205 = 77,205 : x
  2. Step 2: Convert to fraction form
    51,470/77,205 = 77,205/x
  3. Step 3: Cross multiply
    51,470x = 77,205 × 77,205
  4. Step 4: Simplify right side
    51,470x = 5,960,612,025
  5. Step 5: Solve for x
    x = 5,960,612,025/51,470
  6. Step 6: Final answer
    x = 115,807.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.