17. Jack went on a diet. He started out weighing \( 187 \frac{1}{2} \mathrm{lbs} \). The first week he lost \( 10 \frac{1}{4} \mathrm{lbs} . ; \) the second week he lost \( 9 \frac{3}{8} \mathrm{lbs} \).; the third week he lost \( 5 \frac{3}{4} \mathrm{lbs} . ; \) and the fourth week he lost \( 1 \frac{1}{2} \mathrm{lbs} \). What did he weigh at the end of the fourth week?

To find Jack's weight at the end of the fourth week, we need to first calculate the total weight he lost over the four weeks and then subtract that from his starting weight. 1. **Convert all weights to improper fractions:** - Initial weight: \( 187 \frac{1}{2} = \frac{375}{2} \text{ lbs} \) - Week 1 loss: \( 10 \frac{1}{4} = \frac{41}{4} \text{ lbs} \) - Week 2 loss: \( 9 \frac{3}{8} = \frac{75}{8} \text{ lbs} \) - Week 3 loss: \( 5 \frac{3}{4} = \frac{23}{4} \text{ lbs} \) - Week 4 loss: \( 1 \frac{1}{2} = \frac{3}{2} \text{ lbs} \) 2. **Finding a common denominator (which is 8) for the losses:** - Week 1 loss: \( \frac{41}{4} = \frac{82}{8} \) - Week 2 loss: \( \frac{75}{8} \) - Week 3 loss: \( \frac{23}{4} = \frac{46}{8} \) - Week 4 loss: \( \frac{3}{2} = \frac{12}{8} \) 3. **Adding the weekly losses:** \[ \frac{82}{8} + \frac{75}{8} + \frac{46}{8} + \frac{12}{8} = \frac{215}{8} \text{ lbs} \] 4. **Subtracting total weight lost from initial weight:** - Convert initial weight to eighths: \( \frac{375}{2} = \frac{1500}{8} \) 5. **Final weight after 4 weeks:** \[ \frac{1500}{8} - \frac{215}{8} = \frac{1285}{8} \] Converting to a mixed number: \[ \frac{1285}{8} = 160 \frac{5}{8} \text{ lbs} \] At the end of the fourth week, Jack weighed \( 160 \frac{5}{8} \text{ lbs} \).