A movie theater has a seating capacity of 257. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are h

Question

A movie theater has a seating capacity of 257. 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 $ 1860, How many children, students, and adults attended? children attended. students attended. adults attended.

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Delilah 2 months 2021-09-26T00:21:48+00:00 1 Answer 0 views 0

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    2021-09-26T00:23:46+00:00

    Answer:

    Children = 122

    Students = 74

    Adults = 61

    Step-by-step explanation:

    Given

    Seating capacity = 257

    Charges: Children = $5.00; Students = $7.00; Adults = $12.00

    Total sales of ticket = $1860

    Required:

    Number of children, students and adults present in the theatre.

    Let A, C and S represent adult, children and student respectively.

    There are half as many adults as there are children; this means that

    A = ½C

    If the total seat capacity is 257, then

    A + C + S = 257

    Also, if the total sales of tickets is $1860, then

    12A + 7S + 5C = 1860

    So, we have two equations to be solved simultaneously.

    A + C + S = 257 — (1)

    12A + 7S + 5C = 1860 — (2)

    Substitute ½C for A in (1) and (2)

    ½C + C + S = 257

    Multiply both sides by 2

    2(½C + C + S) = 2 * 257

    C + 2C + 2S = 514

    3C + 2S = 514 —– (3)

    12(½C) + 7S + 5C = 1860

    6C + 7S + 5C ,= 1860

    6C + 5C + 7S = 1860

    11C + 7S = 1860 — (4)

    Make S the subject of formula in (3)

    2S = 514 – 3C

    S = ½(514 – 3C)

    S = 257 – 1.5C

    Substituton 257 – 1.5C for S in (4)

    11C + 7(257- 1.5C) = 1860

    11C + 1799 – 10.5C = 1860

    Collect like terms

    11C – 10.5C = 1860 – 1799

    0.5C = 61

    Multiply both sides by 2

    2 * 0.5C = 2 * 61

    C = 122

    Recall that

    S = 257 – 1.5C

    S = 257 – 1.5(122)

    S = 257 – 183

    S = 74

    Also recall that

    A = ½C

    A = ½ * 122

    A = 61

    Hence the attendance at the mobie theatre are;

    Children = 122

    Students = 74

    Adults = 61

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