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Finding the Third Proportional to 512 and 1,106

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Solution

The third proportional to 512 and 1,106 is: 2,389.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    512 : 1,106 = 1,106 : x
  2. Step 2: Convert to fraction form
    512/1,106 = 1,106/x
  3. Step 3: Cross multiply
    512x = 1,106 × 1,106
  4. Step 4: Simplify right side
    512x = 1,223,236
  5. Step 5: Solve for x
    x = 1,223,236/512
  6. Step 6: Final answer
    x = 2,389.13

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.