Every weekday Lidija spends \( \frac{1}{2} \) an hour at the gym when she gets back from school. On each day of the weekend she spends \( 2 \frac{5}{6} \) hours at the gym. How many hours does she spend at the gym in total each week? INSTRUCTION: Give your answer as a mixed number (do not round off).

To find out how many hours Lidija spends at the gym in a week, we can break it down into weekdays and the weekend. During the weekdays (Monday to Friday), Lidija spends \( \frac{1}{2} \) an hour each day, which totals to: \[ 5 \times \frac{1}{2} = \frac{5}{2} \text{ hours} \] On the weekends, she spends \( 2 \frac{5}{6} \) hours each day, which is \( \frac{17}{6} \) when converted to an improper fraction (since \( 2 \frac{5}{6} = 2 + \frac{5}{6} = \frac{12}{6} + \frac{5}{6} \)). Thus, over the weekend (Saturday and Sunday), she spends: \[ 2 \times \frac{17}{6} = \frac{34}{6} = \frac{17}{3} \text{ hours} \] Now, we add her time spent during the weekdays to her weekend time: \[ \frac{5}{2} + \frac{17}{3} \] To add these fractions, we need a common denominator, which is 6. Converting each fraction, we get: \[ \frac{5}{2} = \frac{15}{6} \quad \text{and} \quad \frac{17}{3} = \frac{34}{6} \] Now, we add them: \[ \frac{15}{6} + \frac{34}{6} = \frac{49}{6} \] Finally, to convert \( \frac{49}{6} \) into a mixed number: \[ \frac{49}{6} = 8 \frac{1}{6} \] So, Lidija spends a total of \( 8 \frac{1}{6} \) hours at the gym each week.