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Finding the Third Proportional to 4,142 and 8,564

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Solution

The third proportional to 4,142 and 8,564 is: 17,706.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,142 : 8,564 = 8,564 : x
  2. Step 2: Convert to fraction form
    4,142/8,564 = 8,564/x
  3. Step 3: Cross multiply
    4,142x = 8,564 × 8,564
  4. Step 4: Simplify right side
    4,142x = 73,342,096
  5. Step 5: Solve for x
    x = 73,342,096/4,142
  6. Step 6: Final answer
    x = 17,706.93

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.