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Finding the Third Proportional to 2,034 and 3,140

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Solution

The third proportional to 2,034 and 3,140 is: 4,847.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,034 : 3,140 = 3,140 : x
  2. Step 2: Convert to fraction form
    2,034/3,140 = 3,140/x
  3. Step 3: Cross multiply
    2,034x = 3,140 × 3,140
  4. Step 4: Simplify right side
    2,034x = 9,859,600
  5. Step 5: Solve for x
    x = 9,859,600/2,034
  6. Step 6: Final answer
    x = 4,847.39

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.