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Finding the Third Proportional to 1,964 and 4,207

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Solution

The third proportional to 1,964 and 4,207 is: 9,011.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,964 : 4,207 = 4,207 : x
  2. Step 2: Convert to fraction form
    1,964/4,207 = 4,207/x
  3. Step 3: Cross multiply
    1,964x = 4,207 × 4,207
  4. Step 4: Simplify right side
    1,964x = 17,698,849
  5. Step 5: Solve for x
    x = 17,698,849/1,964
  6. Step 6: Final answer
    x = 9,011.63

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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.