To find an equivalent equation that Eileen's method solves, we can start with the steps she took:
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She added 38 to 176: \[ 176 + 38 = 214 \]
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Then she divided the sum by 6: \[ \frac{214}{6} = \frac{107}{3} \approx 35.67 \]
Now we want to establish an equation that results in \(m = \frac{107}{3}\).
Since she divided the sum (214) by 6, we can reverse this operation to find an equation involving \(m\): \[ m = \frac{214}{6} \] To eliminate the division, multiply both sides by 6: \[ 6m = 214 \]
Now, since we need 214 in terms of adding or subtracting other values to equal 176, we can incorporate 38. Rearranging gives: \[ 6m = 176 + 38 \]
So the equivalent equation represented in the answer choices is: \[ 6m + 38 = 176 \]
Thus, the correct option is: 6m + 38 = 176.