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Finding the Third Proportional to 216 and 514

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Solution

The third proportional to 216 and 514 is: 1,223.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    216 : 514 = 514 : x
  2. Step 2: Convert to fraction form
    216/514 = 514/x
  3. Step 3: Cross multiply
    216x = 514 × 514
  4. Step 4: Simplify right side
    216x = 264,196
  5. Step 5: Solve for x
    x = 264,196/216
  6. Step 6: Final answer
    x = 1,223.13

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.