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Finding the Third Proportional to 102,096 and 216,315

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Solution

The third proportional to 102,096 and 216,315 is: 458,315.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,096 : 216,315 = 216,315 : x
  2. Step 2: Convert to fraction form
    102,096/216,315 = 216,315/x
  3. Step 3: Cross multiply
    102,096x = 216,315 × 216,315
  4. Step 4: Simplify right side
    102,096x = 46,792,179,225
  5. Step 5: Solve for x
    x = 46,792,179,225/102,096
  6. Step 6: Final answer
    x = 458,315.50

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.