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Finding the Third Proportional to 12,196 and 19,378

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Solution

The third proportional to 12,196 and 19,378 is: 30,789.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,196 : 19,378 = 19,378 : x
  2. Step 2: Convert to fraction form
    12,196/19,378 = 19,378/x
  3. Step 3: Cross multiply
    12,196x = 19,378 × 19,378
  4. Step 4: Simplify right side
    12,196x = 375,506,884
  5. Step 5: Solve for x
    x = 375,506,884/12,196
  6. Step 6: Final answer
    x = 30,789.35

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.