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Finding the Third Proportional to 5,824 and 6,304

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Solution

The third proportional to 5,824 and 6,304 is: 6,823.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,824 : 6,304 = 6,304 : x
  2. Step 2: Convert to fraction form
    5,824/6,304 = 6,304/x
  3. Step 3: Cross multiply
    5,824x = 6,304 × 6,304
  4. Step 4: Simplify right side
    5,824x = 39,740,416
  5. Step 5: Solve for x
    x = 39,740,416/5,824
  6. Step 6: Final answer
    x = 6,823.56

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.