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Finding the Third Proportional to 256,196 and 409,278

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Solution

The third proportional to 256,196 and 409,278 is: 653,829.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,196 : 409,278 = 409,278 : x
  2. Step 2: Convert to fraction form
    256,196/409,278 = 409,278/x
  3. Step 3: Cross multiply
    256,196x = 409,278 × 409,278
  4. Step 4: Simplify right side
    256,196x = 167,508,481,284
  5. Step 5: Solve for x
    x = 167,508,481,284/256,196
  6. Step 6: Final answer
    x = 653,829.42

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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.