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Finding the Third Proportional to 1,409 and 2,991

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Solution

The third proportional to 1,409 and 2,991 is: 6,349.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,409 : 2,991 = 2,991 : x
  2. Step 2: Convert to fraction form
    1,409/2,991 = 2,991/x
  3. Step 3: Cross multiply
    1,409x = 2,991 × 2,991
  4. Step 4: Simplify right side
    1,409x = 8,946,081
  5. Step 5: Solve for x
    x = 8,946,081/1,409
  6. Step 6: Final answer
    x = 6,349.24

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.