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Finding the Third Proportional to 971.81 and 1,413.84

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Solution

The third proportional to 971.81 and 1,413.84 is: 2,056.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    971.81 : 1,413.84 = 1,413.84 : x
  2. Step 2: Convert to fraction form
    971.81/1,413.84 = 1,413.84/x
  3. Step 3: Cross multiply
    971.81x = 1,413.84 × 1,413.84
  4. Step 4: Simplify right side
    971.81x = 1,998,954.15
  5. Step 5: Solve for x
    x = 1,998,954.15/971.81
  6. Step 6: Final answer
    x = 2,056.93

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.