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Finding the Third Proportional to 1,760 and 3,178

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Solution

The third proportional to 1,760 and 3,178 is: 5,738.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,760 : 3,178 = 3,178 : x
  2. Step 2: Convert to fraction form
    1,760/3,178 = 3,178/x
  3. Step 3: Cross multiply
    1,760x = 3,178 × 3,178
  4. Step 4: Simplify right side
    1,760x = 10,099,684
  5. Step 5: Solve for x
    x = 10,099,684/1,760
  6. Step 6: Final answer
    x = 5,738.46

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Why These Related Problems?

These problems maintain the same ratio (1.81) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.