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Finding the Third Proportional to 416,669 and 589,971

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Solution

The third proportional to 416,669 and 589,971 is: 835,353.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    416,669 : 589,971 = 589,971 : x
  2. Step 2: Convert to fraction form
    416,669/589,971 = 589,971/x
  3. Step 3: Cross multiply
    416,669x = 589,971 × 589,971
  4. Step 4: Simplify right side
    416,669x = 348,065,780,841
  5. Step 5: Solve for x
    x = 348,065,780,841/416,669
  6. Step 6: Final answer
    x = 835,353.20

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.