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Finding the Third Proportional to 7,824 and 15,984

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Solution

The third proportional to 7,824 and 15,984 is: 32,654.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,824 : 15,984 = 15,984 : x
  2. Step 2: Convert to fraction form
    7,824/15,984 = 15,984/x
  3. Step 3: Cross multiply
    7,824x = 15,984 × 15,984
  4. Step 4: Simplify right side
    7,824x = 255,488,256
  5. Step 5: Solve for x
    x = 255,488,256/7,824
  6. Step 6: Final answer
    x = 32,654.43

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.