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Finding the Third Proportional to 564 and 1,142

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Solution

The third proportional to 564 and 1,142 is: 2,312.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    564 : 1,142 = 1,142 : x
  2. Step 2: Convert to fraction form
    564/1,142 = 1,142/x
  3. Step 3: Cross multiply
    564x = 1,142 × 1,142
  4. Step 4: Simplify right side
    564x = 1,304,164
  5. Step 5: Solve for x
    x = 1,304,164/564
  6. Step 6: Final answer
    x = 2,312.35

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.