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Finding the Third Proportional to 1,196 and 2,909

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Solution

The third proportional to 1,196 and 2,909 is: 7,075.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,196 : 2,909 = 2,909 : x
  2. Step 2: Convert to fraction form
    1,196/2,909 = 2,909/x
  3. Step 3: Cross multiply
    1,196x = 2,909 × 2,909
  4. Step 4: Simplify right side
    1,196x = 8,462,281
  5. Step 5: Solve for x
    x = 8,462,281/1,196
  6. Step 6: Final answer
    x = 7,075.49

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.