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Finding the Third Proportional to 5,314 and 6,196

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Solution

The third proportional to 5,314 and 6,196 is: 7,224.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,314 : 6,196 = 6,196 : x
  2. Step 2: Convert to fraction form
    5,314/6,196 = 6,196/x
  3. Step 3: Cross multiply
    5,314x = 6,196 × 6,196
  4. Step 4: Simplify right side
    5,314x = 38,390,416
  5. Step 5: Solve for x
    x = 38,390,416/5,314
  6. Step 6: Final answer
    x = 7,224.39

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.