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Finding the Third Proportional to 213 and 302.25

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Solution

The third proportional to 213 and 302.25 is: 428.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 302.25 = 302.25 : x
  2. Step 2: Convert to fraction form
    213/302.25 = 302.25/x
  3. Step 3: Cross multiply
    213x = 302.25 × 302.25
  4. Step 4: Simplify right side
    213x = 91,355.06
  5. Step 5: Solve for x
    x = 91,355.06/213
  6. Step 6: Final answer
    x = 428.90

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.