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Finding the Third Proportional to 538 and 1,178.75

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Solution

The third proportional to 538 and 1,178.75 is: 2,582.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    538 : 1,178.75 = 1,178.75 : x
  2. Step 2: Convert to fraction form
    538/1,178.75 = 1,178.75/x
  3. Step 3: Cross multiply
    538x = 1,178.75 × 1,178.75
  4. Step 4: Simplify right side
    538x = 1,389,451.56
  5. Step 5: Solve for x
    x = 1,389,451.56/538
  6. Step 6: Final answer
    x = 2,582.62

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.