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Finding the Third Proportional to 7,828 and 17,407

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Solution

The third proportional to 7,828 and 17,407 is: 38,707.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,828 : 17,407 = 17,407 : x
  2. Step 2: Convert to fraction form
    7,828/17,407 = 17,407/x
  3. Step 3: Cross multiply
    7,828x = 17,407 × 17,407
  4. Step 4: Simplify right side
    7,828x = 303,003,649
  5. Step 5: Solve for x
    x = 303,003,649/7,828
  6. Step 6: Final answer
    x = 38,707.67

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.