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Finding the Third Proportional to 142,509 and 200,409

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Solution

The third proportional to 142,509 and 200,409 is: 281,833.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    142,509 : 200,409 = 200,409 : x
  2. Step 2: Convert to fraction form
    142,509/200,409 = 200,409/x
  3. Step 3: Cross multiply
    142,509x = 200,409 × 200,409
  4. Step 4: Simplify right side
    142,509x = 40,163,767,281
  5. Step 5: Solve for x
    x = 40,163,767,281/142,509
  6. Step 6: Final answer
    x = 281,833.20

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.