Two families go to the cinema.
the smith family buy tickets for 1 adult and 4 children and pay £19
the jones family buy tickets for 2 adults and 2 children and pay £17
what is the cost of one child's ticket?
me

x= cost of 1 adult ticket
y=cost of 1 kid ticket
so 1 adult+4 childeren=x+4y=19
2 adults and 2 childern=2x+2y=17
elimination

x+4y=19
2x+2y=17
multiply firest equation by -2
-2x-8y=-38
add to first equatuion
-2x-8y=-38
2x+2y=17 +
0x-6y=21
-6y=-21
multiply -2
6y=21
divide by 6
y=21/6=7/2

subsitute
2x+2y=17
2x+2(7/2)=17
2x+14/2=17
2x+7=17
subtract 7 from both sides
2x=10
divide by 2
x=5

1 adult ticket costs £5
1 kid ticket costs £7/2 or £3 and 1/2 or £3.5

Is there more to the question?

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