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Finding the Third Proportional to 2,098 and 2,284

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Solution

The third proportional to 2,098 and 2,284 is: 2,486.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,098 : 2,284 = 2,284 : x
  2. Step 2: Convert to fraction form
    2,098/2,284 = 2,284/x
  3. Step 3: Cross multiply
    2,098x = 2,284 × 2,284
  4. Step 4: Simplify right side
    2,098x = 5,216,656
  5. Step 5: Solve for x
    x = 5,216,656/2,098
  6. Step 6: Final answer
    x = 2,486.49

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.