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Finding the Third Proportional to 513.84 and 677.74

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Solution

The third proportional to 513.84 and 677.74 is: 893.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    513.84 : 677.74 = 677.74 : x
  2. Step 2: Convert to fraction form
    513.84/677.74 = 677.74/x
  3. Step 3: Cross multiply
    513.84x = 677.74 × 677.74
  4. Step 4: Simplify right side
    513.84x = 459,334.47
  5. Step 5: Solve for x
    x = 459,334.47/513.84
  6. Step 6: Final answer
    x = 893.92

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.