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Finding the Third Proportional to 824 and 1,408

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Solution

The third proportional to 824 and 1,408 is: 2,405.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    824 : 1,408 = 1,408 : x
  2. Step 2: Convert to fraction form
    824/1,408 = 1,408/x
  3. Step 3: Cross multiply
    824x = 1,408 × 1,408
  4. Step 4: Simplify right side
    824x = 1,982,464
  5. Step 5: Solve for x
    x = 1,982,464/824
  6. Step 6: Final answer
    x = 2,405.90

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Why These Related Problems?

These problems maintain the same ratio (1.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.