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Finding the Third Proportional to 2,038 and 4,213

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Solution

The third proportional to 2,038 and 4,213 is: 8,709.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,038 : 4,213 = 4,213 : x
  2. Step 2: Convert to fraction form
    2,038/4,213 = 4,213/x
  3. Step 3: Cross multiply
    2,038x = 4,213 × 4,213
  4. Step 4: Simplify right side
    2,038x = 17,749,369
  5. Step 5: Solve for x
    x = 17,749,369/2,038
  6. Step 6: Final answer
    x = 8,709.21

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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.