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Finding the Third Proportional to 7,214 and 7,838

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Solution

The third proportional to 7,214 and 7,838 is: 8,515.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,214 : 7,838 = 7,838 : x
  2. Step 2: Convert to fraction form
    7,214/7,838 = 7,838/x
  3. Step 3: Cross multiply
    7,214x = 7,838 × 7,838
  4. Step 4: Simplify right side
    7,214x = 61,434,244
  5. Step 5: Solve for x
    x = 61,434,244/7,214
  6. Step 6: Final answer
    x = 8,515.98

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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.