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Finding the Third Proportional to 1,569 and 2,196

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Solution

The third proportional to 1,569 and 2,196 is: 3,073.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,569 : 2,196 = 2,196 : x
  2. Step 2: Convert to fraction form
    1,569/2,196 = 2,196/x
  3. Step 3: Cross multiply
    1,569x = 2,196 × 2,196
  4. Step 4: Simplify right side
    1,569x = 4,822,416
  5. Step 5: Solve for x
    x = 4,822,416/1,569
  6. Step 6: Final answer
    x = 3,073.56

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.