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Finding the Third Proportional to 645 and 1,412.25

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Solution

The third proportional to 645 and 1,412.25 is: 3,092.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    645 : 1,412.25 = 1,412.25 : x
  2. Step 2: Convert to fraction form
    645/1,412.25 = 1,412.25/x
  3. Step 3: Cross multiply
    645x = 1,412.25 × 1,412.25
  4. Step 4: Simplify right side
    645x = 1,994,450.06
  5. Step 5: Solve for x
    x = 1,994,450.06/645
  6. Step 6: Final answer
    x = 3,092.17

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.