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Finding the Third Proportional to 3,136 and 6,784

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Solution

The third proportional to 3,136 and 6,784 is: 14,675.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,136 : 6,784 = 6,784 : x
  2. Step 2: Convert to fraction form
    3,136/6,784 = 6,784/x
  3. Step 3: Cross multiply
    3,136x = 6,784 × 6,784
  4. Step 4: Simplify right side
    3,136x = 46,022,656
  5. Step 5: Solve for x
    x = 46,022,656/3,136
  6. Step 6: Final answer
    x = 14,675.59

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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.