Write a linear system of equations that can be used to solve these problems. Then, solve to get your final answer.
3. The school that Kevin goes to is selling tickets to a fieldtrip. On the first day of ticket sales, the school sold 3 adult tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 adult tickets and 2 child tickets. Find the price of an adult ticket and the price of a child ticket
First of all define your unknowns
let the cost of an adult ticket be x
let the cost ofa child ticket be by
Now translate your English sentences into math:
"first day of ticket sales, the school sold 3 adult tickets and 1 child ticket for a total of $38"
----> 3x + y = 38
"..$52 on the second day by selling 3 adult tickets and 2 child tickets"
---> 3x+2y=52
easiest way is to subtract the first from the 2nd
---> 0 + y = 14
sub that back into the first equation to get the x
Quite easy, right ?
Let's set up a linear system of equations to solve this problem. Let x be the price of an adult ticket and y be the price of a child ticket.
From the information given, we can derive two equations:
Equation 1: 3x + y = 38 (the total sales from the first day)
Equation 2: 3x + 2y = 52 (the total sales from the second day)
To solve the system of equations, we can use various methods such as substitution, elimination, or matrices. I'll use the method of substitution to solve it.
Let's solve Equation 1 for y:
y = 38 - 3x
Substitute this value of y into Equation 2:
3x + 2(38 - 3x) = 52
Now, simplify and solve for x:
3x + 76 - 6x = 52
-3x + 76 = 52
-3x = 52 - 76
-3x = -24
x = (-24)/(-3)
x = 8
Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y:
3(8) + y = 38
24 + y = 38
y = 38 - 24
y = 14
Therefore, the price of an adult ticket is $8, and the price of a child ticket is $14