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Finding the Third Proportional to 213 and 564

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Solution

The third proportional to 213 and 564 is: 1,493.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 564 = 564 : x
  2. Step 2: Convert to fraction form
    213/564 = 564/x
  3. Step 3: Cross multiply
    213x = 564 × 564
  4. Step 4: Simplify right side
    213x = 318,096
  5. Step 5: Solve for x
    x = 318,096/213
  6. Step 6: Final answer
    x = 1,493.41

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Why These Related Problems?

These problems maintain the same ratio (2.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.