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Finding the Third Proportional to 1,209 and 1,638

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Solution

The third proportional to 1,209 and 1,638 is: 2,219.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,209 : 1,638 = 1,638 : x
  2. Step 2: Convert to fraction form
    1,209/1,638 = 1,638/x
  3. Step 3: Cross multiply
    1,209x = 1,638 × 1,638
  4. Step 4: Simplify right side
    1,209x = 2,683,044
  5. Step 5: Solve for x
    x = 2,683,044/1,209
  6. Step 6: Final answer
    x = 2,219.23

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.