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Finding the Third Proportional to 461 and 1,007

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Solution

The third proportional to 461 and 1,007 is: 2,199.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    461 : 1,007 = 1,007 : x
  2. Step 2: Convert to fraction form
    461/1,007 = 1,007/x
  3. Step 3: Cross multiply
    461x = 1,007 × 1,007
  4. Step 4: Simplify right side
    461x = 1,014,049
  5. Step 5: Solve for x
    x = 1,014,049/461
  6. Step 6: Final answer
    x = 2,199.67

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.