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Finding the Third Proportional to 2,560 and 4,106

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Solution

The third proportional to 2,560 and 4,106 is: 6,585.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,560 : 4,106 = 4,106 : x
  2. Step 2: Convert to fraction form
    2,560/4,106 = 4,106/x
  3. Step 3: Cross multiply
    2,560x = 4,106 × 4,106
  4. Step 4: Simplify right side
    2,560x = 16,859,236
  5. Step 5: Solve for x
    x = 16,859,236/2,560
  6. Step 6: Final answer
    x = 6,585.64

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.