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Finding the Third Proportional to 542 and 597.50

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Solution

The third proportional to 542 and 597.50 is: 658.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    542 : 597.50 = 597.50 : x
  2. Step 2: Convert to fraction form
    542/597.50 = 597.50/x
  3. Step 3: Cross multiply
    542x = 597.50 × 597.50
  4. Step 4: Simplify right side
    542x = 357,006.25
  5. Step 5: Solve for x
    x = 357,006.25/542
  6. Step 6: Final answer
    x = 658.68

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These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.