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Finding the Third Proportional to 1,209 and 2,964

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Solution

The third proportional to 1,209 and 2,964 is: 7,266.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,209 : 2,964 = 2,964 : x
  2. Step 2: Convert to fraction form
    1,209/2,964 = 2,964/x
  3. Step 3: Cross multiply
    1,209x = 2,964 × 2,964
  4. Step 4: Simplify right side
    1,209x = 8,785,296
  5. Step 5: Solve for x
    x = 8,785,296/1,209
  6. Step 6: Final answer
    x = 7,266.58

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Why These Related Problems?

These problems maintain the same ratio (2.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.