In Exercises 33–41, use the four-step strategy to solve each problem. Use x, y, and z to represent unknown quantities. Then translate from the verbal conditions of the problem to a system of three equations in three variables.

The bar graph shows the average number of hours U.S. college students study per week for seven selected majors. Study times are rounded to the nearest hour.The combined weekly study time for students majoring in chemical engineering, mathematics, and psychology is 52 hours. The difference between weekly study time for chemical engineering majors and math majors is 6 hours. The difference between weekly study time for chemical engineering majors and psychology majors is 8 hours. Find the average number of hours per week that chemical engineering majors, mathematics majors, and psychology majors spend studying.

Hours Spent Studying per Week 12 L Number of Hours U.S. College Students Study per Week, by Major 24 Architecture Chemical Engineering 18 Nursing Mathematics ******* Major Psychology 12 Physical Education Speech