Linear equations

Question

A movie theater has a seating capacity of 211. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1526, How many children, students, and adults attended?

Answer 1

A=C/2 A=adults, C=children S=students

A+C+S=211

C/2 + C + S = 211

(3/2)C + S = 211

S= 211 - (3/2)C

5C+7S+12A=1526

5C + 7(211-(3/2)C) +12(C/2) = 1526

C/2 + 1477 = 1526

C/2 = 1526-1477 = 49

C=2(49) = 98 children

A=C/2 = 98/2 = 49 adults

S= 211 -(3/2)C = 211 -147 = 64 students

98+49+64 = 211