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Finding the Third Proportional to 105,824 and 220,416

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Solution

The third proportional to 105,824 and 220,416 is: 459,094.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,824 : 220,416 = 220,416 : x
  2. Step 2: Convert to fraction form
    105,824/220,416 = 220,416/x
  3. Step 3: Cross multiply
    105,824x = 220,416 × 220,416
  4. Step 4: Simplify right side
    105,824x = 48,583,213,056
  5. Step 5: Solve for x
    x = 48,583,213,056/105,824
  6. Step 6: Final answer
    x = 459,094.47

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.