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Finding the Third Proportional to 1,023.26 and 1,584.14

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Solution

The third proportional to 1,023.26 and 1,584.14 is: 2,452.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023.26 : 1,584.14 = 1,584.14 : x
  2. Step 2: Convert to fraction form
    1,023.26/1,584.14 = 1,584.14/x
  3. Step 3: Cross multiply
    1,023.26x = 1,584.14 × 1,584.14
  4. Step 4: Simplify right side
    1,023.26x = 2,509,501.52
  5. Step 5: Solve for x
    x = 2,509,501.52/1,023.26
  6. Step 6: Final answer
    x = 2,452.46

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.