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Finding the Third Proportional to 105,865 and 232,465

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Solution

The third proportional to 105,865 and 232,465 is: 510,461.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,865 : 232,465 = 232,465 : x
  2. Step 2: Convert to fraction form
    105,865/232,465 = 232,465/x
  3. Step 3: Cross multiply
    105,865x = 232,465 × 232,465
  4. Step 4: Simplify right side
    105,865x = 54,039,976,225
  5. Step 5: Solve for x
    x = 54,039,976,225/105,865
  6. Step 6: Final answer
    x = 510,461.21

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.