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Finding the Third Proportional to 1,213 and 1,829

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Solution

The third proportional to 1,213 and 1,829 is: 2,757.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,213 : 1,829 = 1,829 : x
  2. Step 2: Convert to fraction form
    1,213/1,829 = 1,829/x
  3. Step 3: Cross multiply
    1,213x = 1,829 × 1,829
  4. Step 4: Simplify right side
    1,213x = 3,345,241
  5. Step 5: Solve for x
    x = 3,345,241/1,213
  6. Step 6: Final answer
    x = 2,757.82

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.