SOLUTION: 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)
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Question 150808: 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?
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
(1) Set up a system of equations to model this scenario.
b=# of boys
g=# of girls
.44b+.35g=231
b+g=615
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(2) how many boys and how many girls were in the survey.
Solve for g in the second equation
g=615-b
plug that in for g in the top equation
.44b+.35(615-b)=231
Distribute
.44b+215.25-.35b=231
Combine like terms
.09b+215.25=231
Subtract 215.25 from both sides
.09b=15.75
Divide each side by .09
b=175
g=615-b
g=615-175
g=440
# of boys=175
# of girls=440
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