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Finding the Third Proportional to 4,596 and 10,164

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Solution

The third proportional to 4,596 and 10,164 is: 22,477.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,596 : 10,164 = 10,164 : x
  2. Step 2: Convert to fraction form
    4,596/10,164 = 10,164/x
  3. Step 3: Cross multiply
    4,596x = 10,164 × 10,164
  4. Step 4: Simplify right side
    4,596x = 103,306,896
  5. Step 5: Solve for x
    x = 103,306,896/4,596
  6. Step 6: Final answer
    x = 22,477.57

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.