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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

APPLICATIONS

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 A X = 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 sales woman earn on each model of cell phone?

To determine

(a)

To find:

A system of equations in x, y, and z.

Explanation

Given:

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. She earns the commission for each cell phone she sells, 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.

Let x, y, and z represent the commission she earns on standard, deluxe, and super-deluxe, respectively.

Approach:

The above information can be represented in a table as written below.

Week Standard
(x)
Deluxe
(y)
Super deluxe
(z)
Commission
($)
First 9
To determine

(b)

To express:

The system of equation found in part (a) as a matrix equation of the form AX=B

To determine

(c)

To find:

The inverse of the coefficient matrix A and use it to solve the matrix equation in part (b). The commission earned by the sales woman on each model of cell phone

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