Question 1204986
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Fact 1: <font color=blue>sold 6 children tickets and 5 adults tickets for a total of $130.00</font>
Fact 2: <font color=blue>school collected $284.00 on the second day by selling 12 children tickets and 13 adult tickets</font>


Fact 1 translates to the equation 6x+5y = 130
Fact 2 translates to the equation 12x+13y = 284
x = price of child ticket
y = price of an adult ticket


Let's double everything in the 1st equation to get 12x+10y = 260


We have this equivalent system
12x+10y = 260
12x+13y = 284


Subtract straight down to get -3y = -24 which solves to y = 8
It costs $8 per adult.


Then use this to find x.
6x+5y = 130
6x+5*8 = 130
6x+40 = 130
6x = 130-40
6x = 90
x = 90/6
x = 15
It costs $15 per child.



<font color=red>Ticket prices:
child = $15
adult = $8</font>
It's interesting that the child ticket costs more compared to the adult, when normally math problems like this have it flipped around (to reflect the real world that does the same thing). Of course these are just hypothetical numbers anyway.


Let's check fact 1
6x+5y = 130
6*15+5*8 = 130
90+40 = 130
130 = 130 ... works out
And now fact 2
12x+13y = 284
12*15+13*8 = 284
180+104 = 284
284 = 284 .... verified as well
The answers are fully confirmed.
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