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Finding the Third Proportional to 213 and 314

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Solution

The third proportional to 213 and 314 is: 462.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    213 : 314 = 314 : x
  2. Step 2: Convert to fraction form
    213/314 = 314/x
  3. Step 3: Cross multiply
    213x = 314 × 314
  4. Step 4: Simplify right side
    213x = 98,596
  5. Step 5: Solve for x
    x = 98,596/213
  6. Step 6: Final answer
    x = 462.89

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These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.