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Finding the Third Proportional to 6,534 and 7,074

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Solution

The third proportional to 6,534 and 7,074 is: 7,658.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,534 : 7,074 = 7,074 : x
  2. Step 2: Convert to fraction form
    6,534/7,074 = 7,074/x
  3. Step 3: Cross multiply
    6,534x = 7,074 × 7,074
  4. Step 4: Simplify right side
    6,534x = 50,041,476
  5. Step 5: Solve for x
    x = 50,041,476/6,534
  6. Step 6: Final answer
    x = 7,658.63

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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.