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3 February, 04:51

Solve this application problem using a system of equations: The Springfield Movie Theater sold adult tickets for $4.10 each and children's tickets for $2.70 each. Last Thursday, a total of $331.30 was collected from 89 movie watchers. How many of each type of ticket were sold on Thursday?

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  1. 3 February, 05:00
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    Answer: 65 adult ticket and 24 children's ticket

    Step-by-step explanation:

    Let the total number of adults be x

    And the total number of children be y

    The cost of ticket for 1 adult = $4.10, this means that the cost of ticket for x adults will be 4.10x

    The cost of ticket for a child = $2.70, this means that the cost of ticket for y children will be 2.70y.

    The total sale was $331.30, that is

    4.10x + 2.70y = 331.30

    Total number of movie watchers were 89, that is

    x + y = 89

    Combining the two equations, we have:

    x + y = 89 ... equation 1

    4.10x + 2.70y = 331.30 ... equation 2

    solving the system of linear equation by substitution method.

    From equation 1, make x the subject of the formula

    x = 89 - y ... equation 3

    substitute x = 89 - y into equation 2, equation 2 then becomes

    4.10 (89 - y) + 2.70y = 331.30

    expanding the bracket, we have

    364.9 - 4.10y + 2.70y = 331.30

    364.9 - 1.4y = 331.30

    collecting the like terms, we have

    364.9 - 331.30 = 1.4y

    33.6 = 1.4y

    divide through by 1.4

    33.6/1.4 = y

    Therefore : y = 24

    substitute y = 24 into equation 3

    x = 89 - y

    x = 89 - 24

    x = 65

    Therefore, there were 65 adults and 24 children ticket sold
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