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Finding the Third Proportional to 1,085 and 1,196

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Solution

The third proportional to 1,085 and 1,196 is: 1,318.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,085 : 1,196 = 1,196 : x
  2. Step 2: Convert to fraction form
    1,085/1,196 = 1,196/x
  3. Step 3: Cross multiply
    1,085x = 1,196 × 1,196
  4. Step 4: Simplify right side
    1,085x = 1,430,416
  5. Step 5: Solve for x
    x = 1,430,416/1,085
  6. Step 6: Final answer
    x = 1,318.36

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.