To find an equation that gives the same result as Eileen's method, we can break down her steps:
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Eileen first added 38 to 176: \[ 176 + 38 = 214 \]
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Then she divided the sum by 6: \[ \frac{214}{6} = \frac{107}{3} \]
We need to create an equation involving \( m \) that leads to the same result:
Starting from her process, we know: \[ \frac{176 + 38}{6} = m \]
We can multiply both sides by 6 to eliminate the fraction: \[ 176 + 38 = 6m \]
Now simplifying the left side: \[ 214 = 6m \]
Now we can rearrange this to form an equation: \[ 6m = 214 \]
Equating it with correct options, we need to express 214 in terms of other setups. Let's consider the possible answer choices:
- 6m + 38 = 176 → This is incorrect because it doesn't match the derived equation.
- 6m − 38 = 176 → This is incorrect since rearranging would not yield 6m = 214.
- 6(m − 38) = 176 → This is also incorrect because it reverts to 6m.
- 6(m + 38) = 176 → Solving would lead to \(6m + 228 = 176\), or \(6m = -52\), which doesn't match.
After evaluating, the correct transformation leads to:
\[ 6m = 214 \Rightarrow \frac{214}{6} = m \]
None of the provided options directly relate to the correct solution derived, thus, the options must be re-examined.
If we were to create an equation that solves directly to Eileen's division setup without conflict:
- It should be simply set up from \( 6m = 214 \), preferably from rearrangement.
So to conclude:
- Since we want the equation which is equivalent to Eileen's method concerning \( m \): Most aligned with Eileen's logic following her addition would translate into \( 6m = 214 \).
None of the options seems to directly match or substitute into the equation derived \( 6m = 214 \) without modifying the original operands' output. Confirm that the selection remains or provides another.
For clarification, if you feel there's a confusion reiterating through steps to attain the solution might clear any misunderstanding.
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