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Finding the Third Proportional to 1,034 and 2,138.50

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Solution

The third proportional to 1,034 and 2,138.50 is: 4,422.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,034 : 2,138.50 = 2,138.50 : x
  2. Step 2: Convert to fraction form
    1,034/2,138.50 = 2,138.50/x
  3. Step 3: Cross multiply
    1,034x = 2,138.50 × 2,138.50
  4. Step 4: Simplify right side
    1,034x = 4,573,182.25
  5. Step 5: Solve for x
    x = 4,573,182.25/1,034
  6. Step 6: Final answer
    x = 4,422.81

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.