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Finding the Third Proportional to 268,096 and 589,184

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Solution

The third proportional to 268,096 and 589,184 is: 1,294,826.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    268,096 : 589,184 = 589,184 : x
  2. Step 2: Convert to fraction form
    268,096/589,184 = 589,184/x
  3. Step 3: Cross multiply
    268,096x = 589,184 × 589,184
  4. Step 4: Simplify right side
    268,096x = 347,137,785,856
  5. Step 5: Solve for x
    x = 347,137,785,856/268,096
  6. Step 6: Final answer
    x = 1,294,826.43

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.