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Finding the Third Proportional to 256,974 and 409,221

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Solution

The third proportional to 256,974 and 409,221 is: 651,668.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,974 : 409,221 = 409,221 : x
  2. Step 2: Convert to fraction form
    256,974/409,221 = 409,221/x
  3. Step 3: Cross multiply
    256,974x = 409,221 × 409,221
  4. Step 4: Simplify right side
    256,974x = 167,461,826,841
  5. Step 5: Solve for x
    x = 167,461,826,841/256,974
  6. Step 6: Final answer
    x = 651,668.37

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.