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Finding the Third Proportional to 7,584 and 14,096

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Solution

The third proportional to 7,584 and 14,096 is: 26,199.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,584 : 14,096 = 14,096 : x
  2. Step 2: Convert to fraction form
    7,584/14,096 = 14,096/x
  3. Step 3: Cross multiply
    7,584x = 14,096 × 14,096
  4. Step 4: Simplify right side
    7,584x = 198,697,216
  5. Step 5: Solve for x
    x = 198,697,216/7,584
  6. Step 6: Final answer
    x = 26,199.53

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.