Question 151348This question is from textbook College Algebra
: HI
can someone please help me with the math results from theses answers Stanbon was nice enough to answers the questions.I would like to see how the answers came about So can someone show me the work so I can understand the final answer for each question. I will resubmit the questions and the answers I recieved
Thank you
Droxygirl001
i) Problem: A survey of 615 teenagers found that 44% of the boys and 35% of the girls would like to be taller. Altogether, 231 teenagers in the survey wished they were taller.
(1) Set up a system of equations to model this scenario.
(2) Use determinants and Cramer’s rule to determine how many boys and how many girls were in the survey.
(3) Answer the question in (2) by using inverse matrices.
(4) Compare the two methods. When might one method be better than another method for solving a system?
THESES ARE THE ANSWERS I RECIEVED
A survey of 615 teenagers found that 44% of the boys and 35% of the girls would like to be taller. Altogether, 231 teenagers in the survey wished they were taller.
(1) Set up a system of equations to model this scenario.
Let the number of boys be "b":
Let the number of girls be "g":
EQUATION:
b + g = 615
0.44b + 0.35g = 231
----------------------------
(2) Use determinants and Cramer’s rule to determine how many boys and how many girls were in the survey.
b = 175
g = 440
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(3) Answer the question in (2) by using inverse matrices.
-------------------------------
(4) Compare the two methods. When might one method be better than another method for solving a system?
Using the inverse method is much faster.
This question is from textbook College Algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Problem: A survey of 615 teenagers found that 44% of the boys and 35% of the girls would like to be taller. Altogether, 231 teenagers in the survey wished they were taller.
(1) Set up a system of equations to model this scenario.
(2) Use determinants and Cramer’s rule to determine how many boys and how many girls were in the survey.
(3) Answer the question in (2) by using inverse matrices.
(4) Compare the two methods. When might one method be better than another method for solving a system?
THESES ARE THE ANSWERS I RECIEVED
A survey of 615 teenagers found that 44% of the boys and 35% of the girls would like to be taller. Altogether, 231 teenagers in the survey wished they were taller.
(1) Set up a system of equations to model this scenario.
Let the number of boys be "b":
Let the number of girls be "g":
EQUATION:
Quantity Equation.............: b + g = 615
"Want to be taller" Equation..:0.44b + 0.35g = 231
----------------------------
(2) Use determinants and Cramer’s rule to determine how many boys and how many girls were in the survey.
The determinant of the coefficients is (1*0.35)-(1*0.44) = -0.09
The "b" determinant is (615*0.35)-(1*231) = -15.7
Then b = (b-determinant)/(coefficient determinant) = 175
---------------
The "g" determinant is (1*231)-(615*0.44) = -39.6
Then g = (g-determinant)/(coefficient determinant) = 440
----------------
b = 175
g = 440
-------------------------
(3) Answer the question in (2) by using inverse matrices.
EQUATION:
Quantity Equation.............: b + g = 615
"Want to be taller" Equation..:0.44b + 0.35g = 231
Write this pair of equations in matrix form:
..1......1....615
.0.44...0.35..231
--------------------
Find the inverse of the coefficient matrix:
inverse is
...-35/9.....100.9
....44.9....-100.9
----------------------
Multiply that inverse matrix times the column vector [615..231]
to get:
b = 175
g = 440
-------------------------------
(4) Compare the two methods. When might one method be better than another method for solving a system?
The inverse matrix method is always faster if you have a calculator.
Cramer's method might be faster if you have only 2 equations with 2
variables and you don't make arithmetic mistakes.
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Cheers,
Stan H.
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