Chapter 6.3, Problem 63E

Sales Commissions A saleswoman works at a kiosk that offers three different models of cell phones: standard with 16 GB capacity, deluxe with 32 GB capacity, and super deluxe with 64 GB capacity. For each phone that she sells, she earns a commission based on the cell phone model. One week she sells 9 standard, 11 deluxe, and 8 super-deluxe and makes $740 in commission. The next week she sells 13 standard, 15 deluxe, and 16 super-deluxe for a $1204 commission. The third week she sells 8 standard, 7 deluxe, and 14 super-deluxe, earning $828 in commission.
 (a) Let x, y, and z represent the commission she earns on standard, deluxe, and super-deluxe, respectively. Translate the given information into a system of equations in x, y, and z.
 (b) Express the system of equations you found in part (a) as a matrix equation of the form $AX=B$ .
 (c) Find the inverse of the coefficient matrix A and use it to solve the matrix equation in part (b). How much commission does the saleswoman earn on each model of cell phone?