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Finding the Third Proportional to 782.25 and 1,212

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Solution

The third proportional to 782.25 and 1,212 is: 1,877.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    782.25 : 1,212 = 1,212 : x
  2. Step 2: Convert to fraction form
    782.25/1,212 = 1,212/x
  3. Step 3: Cross multiply
    782.25x = 1,212 × 1,212
  4. Step 4: Simplify right side
    782.25x = 1,468,944
  5. Step 5: Solve for x
    x = 1,468,944/782.25
  6. Step 6: Final answer
    x = 1,877.84

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.