To find: The system of equation according to given information in term of
Answer to Problem 49E
Explanation of Solution
Given: An encyclopedia saleswoman works for a company that offers three different grades of bindings for its encyclopedias: standard, deluxe and leather. For each set she sells, she earns a commission based on the set’s binding grade. One week she sells one standard, one deluxe and two leather sets and makes $675 in commission. The next week she sells two standard, one deluxe and one leather set for a $600 commission. The third week she sells one standard , two deluxe and one leather earning $625 in commission.
Let
According to question,
First week she sells one standard, one deluxe and two leather sets and makes $675 in commission.
The next week she sells two standard, one deluxe and one leather set for a $600 commission.
The third week she sells one standard , two deluxe and one leather earning $625 in commission.
Hence, the system of equations are
To express: The system of equations in matrix form
Answer to Problem 49E
Explanation of Solution
Given: The system of equations are,
The matrix form
A is matrix form by coefficient of variable
X is matrix of variable.
B is matrix of constant term.
Now using above matrix to write system of equation in matrix form.
To find: The commission of each type of binding.
Answer to Problem 49E
Commission on standard type of encyclopedias binding is $125
Commission on deluxe type of encyclopedias binding is $150
Commission on leather type of encyclopedias binding is $200
Explanation of Solution
Given: The system of equations are,
First find the inverse of this matrix using row-echelon method.
Therefore,
The matrix form of system of equation,
Hence, commission on standard type of encyclopedias binding is $125
Commission on deluxe type of encyclopedias binding is $150
Commission on leather type of encyclopedias binding is $200
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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