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Finding the Third Proportional to 6,824 and 7,784

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Solution

The third proportional to 6,824 and 7,784 is: 8,879.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,824 : 7,784 = 7,784 : x
  2. Step 2: Convert to fraction form
    6,824/7,784 = 7,784/x
  3. Step 3: Cross multiply
    6,824x = 7,784 × 7,784
  4. Step 4: Simplify right side
    6,824x = 60,590,656
  5. Step 5: Solve for x
    x = 60,590,656/6,824
  6. Step 6: Final answer
    x = 8,879.05

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.