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Finding the Third Proportional to 7,824 and 9,488

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Solution

The third proportional to 7,824 and 9,488 is: 11,505.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,824 : 9,488 = 9,488 : x
  2. Step 2: Convert to fraction form
    7,824/9,488 = 9,488/x
  3. Step 3: Cross multiply
    7,824x = 9,488 × 9,488
  4. Step 4: Simplify right side
    7,824x = 90,022,144
  5. Step 5: Solve for x
    x = 90,022,144/7,824
  6. Step 6: Final answer
    x = 11,505.90

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.