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Finding the Third Proportional to 523 and 1,216

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Solution

The third proportional to 523 and 1,216 is: 2,827.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 1,216 = 1,216 : x
  2. Step 2: Convert to fraction form
    523/1,216 = 1,216/x
  3. Step 3: Cross multiply
    523x = 1,216 × 1,216
  4. Step 4: Simplify right side
    523x = 1,478,656
  5. Step 5: Solve for x
    x = 1,478,656/523
  6. Step 6: Final answer
    x = 2,827.26

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.