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Finding the Third Proportional to 144 and 312

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Solution

The third proportional to 144 and 312 is: 676

Step by Step Solution

  1. Step 1: Write the proportion equation
    144 : 312 = 312 : x
  2. Step 2: Convert to fraction form
    144/312 = 312/x
  3. Step 3: Cross multiply
    144x = 312 × 312
  4. Step 4: Simplify right side
    144x = 97,344
  5. Step 5: Solve for x
    x = 97,344/144
  6. Step 6: Final answer
    x = 676

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.