One morning, each member of Manjul’s family drank an $8$-ounce mixture of coffee and milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Manjul drank $\frac{1}{7}$ of the total amount of milk and $\frac{2}{17}$ of the total amount of coffee. How many people are there in Manjul’s family?

Let's think step by step and output the final answer within \boxed{}.
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