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Finding the Third Proportional to 13,205 and 19,213

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Solution

The third proportional to 13,205 and 19,213 is: 27,954.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,205 : 19,213 = 19,213 : x
  2. Step 2: Convert to fraction form
    13,205/19,213 = 19,213/x
  3. Step 3: Cross multiply
    13,205x = 19,213 × 19,213
  4. Step 4: Simplify right side
    13,205x = 369,139,369
  5. Step 5: Solve for x
    x = 369,139,369/13,205
  6. Step 6: Final answer
    x = 27,954.51

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.