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Finding the Third Proportional to 7,570 and 8,242

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Solution

The third proportional to 7,570 and 8,242 is: 8,973.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,570 : 8,242 = 8,242 : x
  2. Step 2: Convert to fraction form
    7,570/8,242 = 8,242/x
  3. Step 3: Cross multiply
    7,570x = 8,242 × 8,242
  4. Step 4: Simplify right side
    7,570x = 67,930,564
  5. Step 5: Solve for x
    x = 67,930,564/7,570
  6. Step 6: Final answer
    x = 8,973.65

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.