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Finding the Third Proportional to 1,670 and 3,178

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Solution

The third proportional to 1,670 and 3,178 is: 6,047.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,670 : 3,178 = 3,178 : x
  2. Step 2: Convert to fraction form
    1,670/3,178 = 3,178/x
  3. Step 3: Cross multiply
    1,670x = 3,178 × 3,178
  4. Step 4: Simplify right side
    1,670x = 10,099,684
  5. Step 5: Solve for x
    x = 10,099,684/1,670
  6. Step 6: Final answer
    x = 6,047.71

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Why These Related Problems?

These problems maintain the same ratio (1.90) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.