To find out how many months Terrell has been with his book club, we first determine his reading rate based on the information provided.
From the initial information, Terrell read a total of 20 books over 10 months. We can calculate his reading rate in books per month as follows:
\[ \text{Reading rate} = \frac{20 \text{ books}}{10 \text{ months}} = 2 \text{ books per month} \]
Now, we know that Terrell has read a total of 24 books. To find out how many months that entails at the rate of 2 books per month, we set up the following equation:
\[ \text{Months} = \frac{\text{Total Books Read}}{\text{Books per Month}} = \frac{24 \text{ books}}{2 \text{ books per month}} = 12 \text{ months} \]
Thus, Terrell has been with his book club for 12 months.
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