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Finding the Third Proportional to 54,199 and 83,412

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Solution

The third proportional to 54,199 and 83,412 is: 128,370.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,199 : 83,412 = 83,412 : x
  2. Step 2: Convert to fraction form
    54,199/83,412 = 83,412/x
  3. Step 3: Cross multiply
    54,199x = 83,412 × 83,412
  4. Step 4: Simplify right side
    54,199x = 6,957,561,744
  5. Step 5: Solve for x
    x = 6,957,561,744/54,199
  6. Step 6: Final answer
    x = 128,370.67

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.