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Finding the Third Proportional to 257.50 and 283.50

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Solution

The third proportional to 257.50 and 283.50 is: 312.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.50 : 283.50 = 283.50 : x
  2. Step 2: Convert to fraction form
    257.50/283.50 = 283.50/x
  3. Step 3: Cross multiply
    257.50x = 283.50 × 283.50
  4. Step 4: Simplify right side
    257.50x = 80,372.25
  5. Step 5: Solve for x
    x = 80,372.25/257.50
  6. Step 6: Final answer
    x = 312.13

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.