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Finding the Third Proportional to 256,206 and 409,290

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Solution

The third proportional to 256,206 and 409,290 is: 653,842.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,206 : 409,290 = 409,290 : x
  2. Step 2: Convert to fraction form
    256,206/409,290 = 409,290/x
  3. Step 3: Cross multiply
    256,206x = 409,290 × 409,290
  4. Step 4: Simplify right side
    256,206x = 167,518,304,100
  5. Step 5: Solve for x
    x = 167,518,304,100/256,206
  6. Step 6: Final answer
    x = 653,842.24

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.