SOLUTION: Formulate a system of equations for the situation below and solve. A theater has a seating capacity of 834 and charges $3 for children, $5 for students, and $7 for adults. At a

Algebra ->  Systems-of-equations -> SOLUTION: Formulate a system of equations for the situation below and solve. A theater has a seating capacity of 834 and charges $3 for children, $5 for students, and $7 for adults. At a       Log On


   

Question 990395: Formulate a system of equations for the situation below and solve.
A theater has a seating capacity of 834 and charges $3 for children, $5 for students, and $7 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $4346. How many children attended the show?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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C=number of children. S=number of students, A=number of adults
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(1/2)(C+S)=A
C+S=2A Use this to substitute for (C+S)
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C+S+A=834
(C+S)+A=834 Substitute for (C+S)
2A+A=834
3A=834
A=278 .
278 Adults attended the show.
Receipts from adults=($7)(278)=$1946
Receipts from students and children=$4346-$1946=$2400
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C+S=834-278
C+S=556
C=556-S Use this to substitute for C
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$3C+$5S=$2400 Substitute for C.
$3(556-S)+$5S=$2400
$1668-$3S+$5S=$2400
$2S=$732
S=366
366 Students attended the show.
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C=556-S=556-366=190
ANSWER: 190 children attended the show.
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CHECK:
C+S+A=834
190+366+278=834
834=834
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$3C+$5S+$7A=$4346
$3(190)+$5(366)+$7(278)=$4346
$570+$1830+$1946=$4346
$4346=$4346
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