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Finding the Third Proportional to 1,824 and 4,209

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Solution

The third proportional to 1,824 and 4,209 is: 9,712.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,824 : 4,209 = 4,209 : x
  2. Step 2: Convert to fraction form
    1,824/4,209 = 4,209/x
  3. Step 3: Cross multiply
    1,824x = 4,209 × 4,209
  4. Step 4: Simplify right side
    1,824x = 17,715,681
  5. Step 5: Solve for x
    x = 17,715,681/1,824
  6. Step 6: Final answer
    x = 9,712.54

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.