Tanya bought five adult tickets and one children's tickets to a movie for $37.10.li bought three adult tickets and five children's tickets for $38.10. find the cost of one adult ticket and the cost of one children's ticket.

Step-by-step explanation:

Let a and c represent the costs of 1 adult and 1 children's ticket, respectively. Then the two purchases can be written as ...

  5a +c = 37.10

  3a +5c = 38.10

Solving this system of equations will give the ticket prices.

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Subtracting the second equation from 5 times the first gives ...

  5(5a +c) -(3a +5c) = 5(37.10) -(38.10)

  22a = 147.40

  a = 6.70

The first equation is useful for finding the value of c:

  5(6.70) +c = 37.10

  c = 3.60 . . . . subtract 33.50

The cost of one adult ticket is $6.70; the cost of one children's ticket is $3.60.

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The two equations can also be solve quickly using a graphing program.