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Finding the Third Proportional to 7,830 and 17,411

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Solution

The third proportional to 7,830 and 17,411 is: 38,715.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,830 : 17,411 = 17,411 : x
  2. Step 2: Convert to fraction form
    7,830/17,411 = 17,411/x
  3. Step 3: Cross multiply
    7,830x = 17,411 × 17,411
  4. Step 4: Simplify right side
    7,830x = 303,142,921
  5. Step 5: Solve for x
    x = 303,142,921/7,830
  6. Step 6: Final answer
    x = 38,715.57

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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.