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Finding the Third Proportional to 213.75 and 312.75

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Solution

The third proportional to 213.75 and 312.75 is: 457.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.75 : 312.75 = 312.75 : x
  2. Step 2: Convert to fraction form
    213.75/312.75 = 312.75/x
  3. Step 3: Cross multiply
    213.75x = 312.75 × 312.75
  4. Step 4: Simplify right side
    213.75x = 97,812.56
  5. Step 5: Solve for x
    x = 97,812.56/213.75
  6. Step 6: Final answer
    x = 457.60

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.