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Finding the Third Proportional to 564.75 and 824.63

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Solution

The third proportional to 564.75 and 824.63 is: 1,204.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    564.75 : 824.63 = 824.63 : x
  2. Step 2: Convert to fraction form
    564.75/824.63 = 824.63/x
  3. Step 3: Cross multiply
    564.75x = 824.63 × 824.63
  4. Step 4: Simplify right side
    564.75x = 680,006.39
  5. Step 5: Solve for x
    x = 680,006.39/564.75
  6. Step 6: Final answer
    x = 1,204.08

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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.