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Finding the Third Proportional to 213 and 409.50

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Solution

The third proportional to 213 and 409.50 is: 787.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 409.50 = 409.50 : x
  2. Step 2: Convert to fraction form
    213/409.50 = 409.50/x
  3. Step 3: Cross multiply
    213x = 409.50 × 409.50
  4. Step 4: Simplify right side
    213x = 167,690.25
  5. Step 5: Solve for x
    x = 167,690.25/213
  6. Step 6: Final answer
    x = 787.28

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Why These Related Problems?

These problems maintain the same ratio (1.92) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.