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Finding the Third Proportional to 177.75 and 413.02

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Solution

The third proportional to 177.75 and 413.02 is: 959.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    177.75 : 413.02 = 413.02 : x
  2. Step 2: Convert to fraction form
    177.75/413.02 = 413.02/x
  3. Step 3: Cross multiply
    177.75x = 413.02 × 413.02
  4. Step 4: Simplify right side
    177.75x = 170,581.91
  5. Step 5: Solve for x
    x = 170,581.91/177.75
  6. Step 6: Final answer
    x = 959.67

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.