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Finding the Third Proportional to 7,580 and 16,213

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Solution

The third proportional to 7,580 and 16,213 is: 34,678.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,580 : 16,213 = 16,213 : x
  2. Step 2: Convert to fraction form
    7,580/16,213 = 16,213/x
  3. Step 3: Cross multiply
    7,580x = 16,213 × 16,213
  4. Step 4: Simplify right side
    7,580x = 262,861,369
  5. Step 5: Solve for x
    x = 262,861,369/7,580
  6. Step 6: Final answer
    x = 34,678.28

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.