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Finding the Third Proportional to 5,297 and 6,197

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Solution

The third proportional to 5,297 and 6,197 is: 7,249.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,297 : 6,197 = 6,197 : x
  2. Step 2: Convert to fraction form
    5,297/6,197 = 6,197/x
  3. Step 3: Cross multiply
    5,297x = 6,197 × 6,197
  4. Step 4: Simplify right side
    5,297x = 38,402,809
  5. Step 5: Solve for x
    x = 38,402,809/5,297
  6. Step 6: Final answer
    x = 7,249.92

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.