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Finding the Third Proportional to 564.19 and 823.22

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Solution

The third proportional to 564.19 and 823.22 is: 1,201.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    564.19 : 823.22 = 823.22 : x
  2. Step 2: Convert to fraction form
    564.19/823.22 = 823.22/x
  3. Step 3: Cross multiply
    564.19x = 823.22 × 823.22
  4. Step 4: Simplify right side
    564.19x = 677,689.11
  5. Step 5: Solve for x
    x = 677,689.11/564.19
  6. Step 6: Final answer
    x = 1,201.18

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.