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Choice C is correct. It’s given that a gym charges its members a onetime $\$36$ enrollment fee and a membership fee of $\$19$ per month. Let $x$ represent the number of months at the gym after which a member will have been charged a total of $\$188$. If there are no charges other than the enrollment fee and the membership fee, the equation $36+19x=188$ can be used to represent this situation. Subtracting $36$ from both sides of this equation yields $19x=152$. Dividing both sides of this equation by $19$ yields $x=8$. Therefore, a member will have been charged a total of $\$188$ after $8$ months at the gym.

Choice A is incorrect. A member will have been charged a total of $\$\left(36+19\times 4\right)$, or $\$112$, after $4$ months at the gym.

Choice B is incorrect. A member will have been charged a total of $\$\left(36+19\times 5\right)$, or $\$131$, after $5$ months at the gym.

Choice D is incorrect. A member will have been charged a total of $\$\left(36+19\times 10\right)$, or $\$226$, after $10$ months at the gym.