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 physics, English, and sociology is 50 hours. The difference between weekly study time for physics majors and English majors is 4 hours. The difference between weekly study time for physics majors and sociology majors is 6 hours. Find the average number of hours per week that physics majors, English majors, and sociology majors spend studying.

Major Physics Art Biology Sociology Hours Spent Studying per Week Communications English Elementary Education 3 ********* ******* 16 12 226 225 om 15 18 ***************** Study per Week, by Major Number of Hours U.S. College Students