Ask Question
4 November, 13:00

A movie theater has a seating capacity of 235. The theater charges $5 for children, $7 for students, and $12 for adults. There are half as many adults as there are children. If the total ticket sales was $1706, How many children, students, and adults attended?

+5
Answers (1)
  1. 4 November, 14:19
    0
    61 adults, 122 children, and 52 students

    Step-by-step explanation:

    Let a = amount of adults, c = amount of children, and s = amount of students.

    Let's go over what we know:

    total amount: 235

    twice as many children as adults

    children: $5

    student: $7

    adult: $12

    Using this information, we can determine the following:

    a = 1/2c

    235 = c + s + a

    1706 = 5c + 7s + 12a

    Since we know a = 1/2c, plug 1/2c in for a. The equations become:

    235 = c + s + 1/2c

    1706 = 5c + 7s + 6c

    Now, solve the inequalities by substitution.

    235 = c + s + 1/2c

    235 = 1 1/2c + s

    -s + 235 = 1 1/2c

    -s = - 235 + 1 1/2c

    s = 235 - 1 1/2c

    Now, plug in the value for s into the other equation.

    1706 = 5c + 7 (235 - 1 1/2c) + 6c

    -5c + 1706 = 7 (235 - 1 1/2c) + 6c

    -5c = - 1706 + 7 (235 - 1 1/2c) + 6c

    -5c = - 1706 + 1645 - 21c/2 + 6c

    -5c = - 61 - 21c/2 + 6c

    -5c = - 61 - 9c/2

    c = 122

    Now, plug in the value for c into the value of s.

    s = 235 - 1 1/2 (122)

    s = 235 - 183

    s = 52

    Finally, plug in the value for c into the value of a.

    a = 1/2 (122)

    a = 61

    To check, add up all values to make sure they equal 235.

    61 + 52 + 122 = 235.

    Therefore, the final answers are 61 adults, 122 children, and 52 students.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A movie theater has a seating capacity of 235. The theater charges $5 for children, $7 for students, and $12 for adults. There are half as ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers