Question

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

Answer 1

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.