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Finding the Third Proportional to 100,138 and 214,492

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Solution

The third proportional to 100,138 and 214,492 is: 459,434.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,138 : 214,492 = 214,492 : x
  2. Step 2: Convert to fraction form
    100,138/214,492 = 214,492/x
  3. Step 3: Cross multiply
    100,138x = 214,492 × 214,492
  4. Step 4: Simplify right side
    100,138x = 46,006,818,064
  5. Step 5: Solve for x
    x = 46,006,818,064/100,138
  6. Step 6: Final answer
    x = 459,434.16

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.