Let's evaluate the expression step by step correctly:
The original expression is: \[ 33 - 11 + 262 \div 34 \]
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Calculate \( 262 \div 34 \): \[ 262 \div 34 = 7.70588235 \] (We will use this value for the final calculation but keep in mind that it will be approximated or rounded depending on the context of the problem.)
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Now we rewrite the expression using this calculated value: \[ 33 - 11 + 7.70588235 \]
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Solve \( 33 - 11 \): \[ 33 - 11 = 22 \]
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Now add \( 22 + 7.70588235 \): \[ 22 + 7.70588235 = 29.70588235 \]
So the result of the original expression \( 33 - 11 + 262 \div 34 \) is approximately \( 29.71 \) (if we round).
Now, let's review Eve's work:
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In Step 1, she has \( 33 - 11 + 262 \div 34 \) and says it equals: \[ 27 - 11 + 236 \div 34 \]
- This step is incorrect. The subtraction should yield \( 22 \) and the division of \( 262 \) should still be there.
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Step 2 shows: \[ 27 - 11 + 72 \div 34 \]
- This does not follow logically from any previous step.
- Continuing through her steps, it appears that she has consistently miscalculated and changed values incorrectly, and the steps do not reflect the computations correctly.
Thus, to conclude, Eve's work contains several mistakes, and her final answer of \( 112 \) is also incorrect based on the computations we worked through. The correct answer to the expression \( 33 - 11 + 262 \div 34 \) should be approximately \( 29.71 \).