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Finding the Third Proportional to 538 and 613

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Solution

The third proportional to 538 and 613 is: 698.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    538 : 613 = 613 : x
  2. Step 2: Convert to fraction form
    538/613 = 613/x
  3. Step 3: Cross multiply
    538x = 613 × 613
  4. Step 4: Simplify right side
    538x = 375,769
  5. Step 5: Solve for x
    x = 375,769/538
  6. Step 6: Final answer
    x = 698.46

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.