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Finding the Third Proportional to 2,174 and 4,656

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Solution

The third proportional to 2,174 and 4,656 is: 9,971.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,174 : 4,656 = 4,656 : x
  2. Step 2: Convert to fraction form
    2,174/4,656 = 4,656/x
  3. Step 3: Cross multiply
    2,174x = 4,656 × 4,656
  4. Step 4: Simplify right side
    2,174x = 21,678,336
  5. Step 5: Solve for x
    x = 21,678,336/2,174
  6. Step 6: Final answer
    x = 9,971.64

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.