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Finding the Third Proportional to 213 and 380

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Solution

The third proportional to 213 and 380 is: 677.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 380 = 380 : x
  2. Step 2: Convert to fraction form
    213/380 = 380/x
  3. Step 3: Cross multiply
    213x = 380 × 380
  4. Step 4: Simplify right side
    213x = 144,400
  5. Step 5: Solve for x
    x = 144,400/213
  6. Step 6: Final answer
    x = 677.93

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These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.