Sue paid $46 for 2 adult and 4 child tickets to a play. karen paid $86 for 4 adult and 7 child tickets to the same play. what is the cost of 1 adult and 1 child ticket?

Step-by-step explanation:

Let a and c represent the costs of adult and child tickets, respectively. Then the two purchases can be described by ...

  2a +4c = 46 . . . . . . Sue's purchase

  4a +7c = 86 . . . . . . Karen's purchase

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The system can be solved by subtracting the second equation from twice the first:

  2(2a +4c) -(4a +7c) = 2(46) -(86)

  c = 6 . . . . . . . simplify

We can substitute this value into half the first equation to find "a".

  a +2(6) = 23

  a = 23 -12 = 11

The cost of 1 adult ticket is $11; the cost of one child ticket is $6.