SOLUTION: Patricia's school is selling tickets to the school play. On the first day of ticket sales the school sold 6 children tickets and 5 adults tickets for a total of $130.00 The school
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Question 1204986: Patricia's school is selling tickets to the school play. On the first day of ticket sales the school sold 6 children tickets and 5 adults tickets for a total of $130.00 The school collected $284.00 on the second day by selling 12 children tickets and 13 adult tickets. What was the price of each type of ticket?
Found 3 solutions by Theo, math_tutor2020, mananth:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = price of a child ticket.
y = price of an adult ticket.
you have two equations that need to be solved simultaneously.
they are:
6x + 5y = 130
12x + 13y = 284
multiply both sides of the first equation by 2 and leave the second equation as is to get:
12x + 10y = 260
12x + 13y = 284
subtract the first equation from the second to get:
3y = 24
solve for y to get y = 8
replace y with 8 in the second equation to get:
12x + 13*8 = 284
simplify to get:
12x + 104 = 284
subtract 104 from both sides of the equation to get:
12x = 180
solve for x to get:
x = 180/12 = 15
you have x = 15 and y = 8
go back to your original equations to see if they are true when you replace x with 15 and y with 8.
the two original equations are:
6x + 5y = 130 becomes 6*15 + 5*8 = 130 which becomes 90 + 40 = 130 which is true.
12x + 13y = 284 becomes 12*15 + 13*8 = 284 which becomes 180 + 104 = 284 which is also true.
the problem is satisfied when x = 15 and y = 8.
that means the price of a child ticket is 15 and the price of an adult ticket is 8.
that's your solution.
this appears to be counter-intuitive as you would expect the child ticket to be less than the adult ticket, but that's the way it worked out.
here's what it looks like on a graph.
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!
Fact 1: sold 6 children tickets and 5 adults tickets for a total of $130.00
Fact 2: school collected $284.00 on the second day by selling 12 children tickets and 13 adult tickets
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.
Ticket prices:
child = $15
adult = $8
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.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Patricia's school is selling tickets to the school play. On the first day of ticket sales the school sold 6 children tickets and 5 adults tickets for a total of $130.00 The school collected $284.00 on the second day by selling 12 children tickets and 13 adult tickets. What was the price of each type of ticket?
On the first day of ticket sales the school sold 6 children tickets and 5 adults tickets for a total of $130.00 The school collected $284.00 on the second day by selling 12 children tickets and 13 adult tickets. What was the price of each type of ticket?
Let price of child's ticket be $x
Let adult ticket cost $y
FIrst day sale
receipts from child tickets + receipts from adult tickets = 130
6x+5y =130-------------------------(1)
Second day sale
12x+13y = 284----------------------(2)
Multiply (1) by 2and subtract (2)
12x+10y=260
12x+13y=284
---------------
-3y = -24
y= 8
substitute 8 in eq(1)
6x+5*8=130
6x+40= 130
6x=90
x=15
the price of a children's ticket is $15, and the price of an adult ticket is $8.
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