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Finding the Third Proportional to 213 and 456.75

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Solution

The third proportional to 213 and 456.75 is: 979.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 456.75 = 456.75 : x
  2. Step 2: Convert to fraction form
    213/456.75 = 456.75/x
  3. Step 3: Cross multiply
    213x = 456.75 × 456.75
  4. Step 4: Simplify right side
    213x = 208,620.56
  5. Step 5: Solve for x
    x = 208,620.56/213
  6. Step 6: Final answer
    x = 979.44

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.