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Finding the Third Proportional to 313.50 and 422.25

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Solution

The third proportional to 313.50 and 422.25 is: 568.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    313.50 : 422.25 = 422.25 : x
  2. Step 2: Convert to fraction form
    313.50/422.25 = 422.25/x
  3. Step 3: Cross multiply
    313.50x = 422.25 × 422.25
  4. Step 4: Simplify right side
    313.50x = 178,295.06
  5. Step 5: Solve for x
    x = 178,295.06/313.50
  6. Step 6: Final answer
    x = 568.72

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.