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Finding the Third Proportional to 2,034 and 3,205

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Solution

The third proportional to 2,034 and 3,205 is: 5,050.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,034 : 3,205 = 3,205 : x
  2. Step 2: Convert to fraction form
    2,034/3,205 = 3,205/x
  3. Step 3: Cross multiply
    2,034x = 3,205 × 3,205
  4. Step 4: Simplify right side
    2,034x = 10,272,025
  5. Step 5: Solve for x
    x = 10,272,025/2,034
  6. Step 6: Final answer
    x = 5,050.16

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.