A package of pill tablets weighs 100 mg . How many tablets are there in the package if each pill weighs \( 1 \frac{2}{3} \mathrm{mg} \) ? Etablets If you have to take 6 pills per day, how many days will the package last you for?

Given that the package weighs \(100 \, \text{mg}\) and each pill weighs \[ 1\frac{2}{3} \, \text{mg}, \] we first convert the mixed number to an improper fraction: \[ 1\frac{2}{3} = \frac{5}{3} \, \text{mg}. \] ### Step 1: Find the Number of Tablets The number of tablets is the total weight divided by the weight of one tablet: \[ \text{Number of tablets} = \frac{100 \, \text{mg}}{\frac{5}{3} \, \text{mg}}. \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ \text{Number of tablets} = 100 \times \frac{3}{5} = \frac{300}{5} = 60. \] So, there are \(60\) tablets in the package. ### Step 2: Determine the Number of Days the Package Will Last If you take \(6\) pills per day, the number of days the package will last is: \[ \text{Number of days} = \frac{60 \, \text{tablets}}{6 \, \text{tablets/day}} = 10 \, \text{days}. \] ### Final Answer There are \(60\) tablets in the package, and the package will last you \(10\) days.