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Finding the Third Proportional to 213 and 384

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Solution

The third proportional to 213 and 384 is: 692.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 384 = 384 : x
  2. Step 2: Convert to fraction form
    213/384 = 384/x
  3. Step 3: Cross multiply
    213x = 384 × 384
  4. Step 4: Simplify right side
    213x = 147,456
  5. Step 5: Solve for x
    x = 147,456/213
  6. Step 6: Final answer
    x = 692.28

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These problems maintain the same ratio (1.80) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.