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Finding the Third Proportional to 7,538 and 17,465

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Solution

The third proportional to 7,538 and 17,465 is: 40,465.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,538 : 17,465 = 17,465 : x
  2. Step 2: Convert to fraction form
    7,538/17,465 = 17,465/x
  3. Step 3: Cross multiply
    7,538x = 17,465 × 17,465
  4. Step 4: Simplify right side
    7,538x = 305,026,225
  5. Step 5: Solve for x
    x = 305,026,225/7,538
  6. Step 6: Final answer
    x = 40,465.14

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.