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Finding the Third Proportional to 1,209 and 1,891

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Solution

The third proportional to 1,209 and 1,891 is: 2,957.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,209 : 1,891 = 1,891 : x
  2. Step 2: Convert to fraction form
    1,209/1,891 = 1,891/x
  3. Step 3: Cross multiply
    1,209x = 1,891 × 1,891
  4. Step 4: Simplify right side
    1,209x = 3,575,881
  5. Step 5: Solve for x
    x = 3,575,881/1,209
  6. Step 6: Final answer
    x = 2,957.72

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.