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Finding the Third Proportional to 413.75 and 980.38

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Solution

The third proportional to 413.75 and 980.38 is: 2,322.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    413.75 : 980.38 = 980.38 : x
  2. Step 2: Convert to fraction form
    413.75/980.38 = 980.38/x
  3. Step 3: Cross multiply
    413.75x = 980.38 × 980.38
  4. Step 4: Simplify right side
    413.75x = 961,135.14
  5. Step 5: Solve for x
    x = 961,135.14/413.75
  6. Step 6: Final answer
    x = 2,322.99

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.