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2 February, 18:40

17. Admission prices to Cinema I to see a movie are $9.50 for an adult and $6.50 for a child. The admission charge at Cinema II is $8.00 per person regardless of age.

a. Write an inequality showing that the prices are cheaper at Cinema I than at Cinema II.

b. If 6 adults and their children go together to see a movie, use the inequality to find how many children must attend for Cinema I to be the better deal.

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Answers (2)
  1. 2 February, 21:32
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    a. 9.5x + 6.5 (x+c) 0

    b. Must be one child more than the no. of adults.

    Step-by-step explanation:

    For Cinema 1:

    for adult = $9.50

    for child = $6.50

    For Cinema 2:

    Per person regardless of age = $8.00

    First of all, we will find out the condition when per person rates in both cinema are equal.

    Assume x = no. of adults

    y = no. of children

    Rate per person in Cinema I = Rate per person in Cinema II

    (9.5x + 6.5y) / (x+y) = 8

    9.5x + 6.5y = 8 (x+y)

    9.5x + 6.5y = 8x + 8y

    9.5x-8x = 8y-6.5y

    => x = y

    So rates are equal when no. of adults equals no. of children

    For Cinema I to have better rates, no. of children should be atleast 1 more than the no. of adult. In this way the rate per person of Cinema I will be less than 8

    Hence we form an inequality when y = x+c and c > 0

    9.5x + 6.5 (x+c) 0

    Hence there must be 1 more children than the no. of adults attending Cinema I for it to be a better deal.
  2. 2 February, 22:20
    0
    9.50a+6.50c < 8.00 (a+c), 6 children

    Step-by-step explanation:

    Let the number of adults be a

    the number of children be c

    Part 1:

    Cinema 1:

    Cost for adults = $9.50 x a = 9.50a

    Cost of children = $6.50 x c = 6.50c

    Total cost = 9.50a+6.50c

    Cinema 2:

    Total cost = 8.00 (a+c)

    The inequality which shows that the cinema I is cheaper

    9.50a+6.50c < 8.00 (a+c)

    9.50a+6.5c<8a+8c

    9.5a-8a<8c-6.5c

    1.5a<1.5c

    a
    Case 2:

    6 adults goes to cinema, let they are accompanied by c number of children

    Cinema 1

    Total cost = 9.5 x 6 + 6.5 x c

    for cinema 2 the total cost will be

    8 (6+c)

    for cinema 1 to be a better deal

    9.5 x 6 + 6.5 x c < 8 (6+c)

    57+6.5c<48+8c

    57-48<8c-6.5c

    9<1.5c

    c>6

    Hence for Cinema 1 to be a better deal, there must be 6 children accompanying them
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