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Finding the Third Proportional to 680.25 and 1,419.63

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Solution

The third proportional to 680.25 and 1,419.63 is: 2,962.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    680.25 : 1,419.63 = 1,419.63 : x
  2. Step 2: Convert to fraction form
    680.25/1,419.63 = 1,419.63/x
  3. Step 3: Cross multiply
    680.25x = 1,419.63 × 1,419.63
  4. Step 4: Simplify right side
    680.25x = 2,015,335.14
  5. Step 5: Solve for x
    x = 2,015,335.14/680.25
  6. Step 6: Final answer
    x = 2,962.64

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.