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Finding the Third Proportional to 812.75 and 1,782.25

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Solution

The third proportional to 812.75 and 1,782.25 is: 3,908.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    812.75 : 1,782.25 = 1,782.25 : x
  2. Step 2: Convert to fraction form
    812.75/1,782.25 = 1,782.25/x
  3. Step 3: Cross multiply
    812.75x = 1,782.25 × 1,782.25
  4. Step 4: Simplify right side
    812.75x = 3,176,415.06
  5. Step 5: Solve for x
    x = 3,176,415.06/812.75
  6. Step 6: Final answer
    x = 3,908.23

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.