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Finding the Third Proportional to 7,829 and 12,224

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Solution

The third proportional to 7,829 and 12,224 is: 19,086.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,829 : 12,224 = 12,224 : x
  2. Step 2: Convert to fraction form
    7,829/12,224 = 12,224/x
  3. Step 3: Cross multiply
    7,829x = 12,224 × 12,224
  4. Step 4: Simplify right side
    7,829x = 149,426,176
  5. Step 5: Solve for x
    x = 149,426,176/7,829
  6. Step 6: Final answer
    x = 19,086.24

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.