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Finding the Third Proportional to 256,971 and 409,216.50

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Solution

The third proportional to 256,971 and 409,216.50 is: 651,661.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,971 : 409,216.50 = 409,216.50 : x
  2. Step 2: Convert to fraction form
    256,971/409,216.50 = 409,216.50/x
  3. Step 3: Cross multiply
    256,971x = 409,216.50 × 409,216.50
  4. Step 4: Simplify right side
    256,971x = 167,458,143,872.25
  5. Step 5: Solve for x
    x = 167,458,143,872.25/256,971
  6. Step 6: Final answer
    x = 651,661.64

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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.