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Finding the Third Proportional to 971.63 and 1,413.56

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Solution

The third proportional to 971.63 and 1,413.56 is: 2,056.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    971.63 : 1,413.56 = 1,413.56 : x
  2. Step 2: Convert to fraction form
    971.63/1,413.56 = 1,413.56/x
  3. Step 3: Cross multiply
    971.63x = 1,413.56 × 1,413.56
  4. Step 4: Simplify right side
    971.63x = 1,998,158.94
  5. Step 5: Solve for x
    x = 1,998,158.94/971.63
  6. Step 6: Final answer
    x = 2,056.51

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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.