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Finding the Third Proportional to 7,824 and 17,964

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Solution

The third proportional to 7,824 and 17,964 is: 41,245.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,824 : 17,964 = 17,964 : x
  2. Step 2: Convert to fraction form
    7,824/17,964 = 17,964/x
  3. Step 3: Cross multiply
    7,824x = 17,964 × 17,964
  4. Step 4: Simplify right side
    7,824x = 322,705,296
  5. Step 5: Solve for x
    x = 322,705,296/7,824
  6. Step 6: Final answer
    x = 41,245.56

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.