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Finding the Third Proportional to 784.13 and 1,823.63

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Solution

The third proportional to 784.13 and 1,823.63 is: 4,241.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    784.13 : 1,823.63 = 1,823.63 : x
  2. Step 2: Convert to fraction form
    784.13/1,823.63 = 1,823.63/x
  3. Step 3: Cross multiply
    784.13x = 1,823.63 × 1,823.63
  4. Step 4: Simplify right side
    784.13x = 3,325,608.14
  5. Step 5: Solve for x
    x = 3,325,608.14/784.13
  6. Step 6: Final answer
    x = 4,241.17

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.