Eileen correctly solved a math problem by first adding 38 to 176, then dividing the sum by 6.

Which equation could be solved to get the same answer?
Responses
6m + 38 = 176

6m − 38 = 176

6(m − 38) = 176

6(m + 38) =176

1 answer

To find an equation that gives the same result as Eileen's method, we can break down her steps:

  1. Eileen first added 38 to 176: \[ 176 + 38 = 214 \]

  2. 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:

  1. 6m + 38 = 176 → This is incorrect because it doesn't match the derived equation.
  2. 6m − 38 = 176 → This is incorrect since rearranging would not yield 6m = 214.
  3. 6(m − 38) = 176 → This is also incorrect because it reverts to 6m.
  4. 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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