Taking into account the definition of a system of linear equations, the number of child tickets sold is 20 and the number of adult tickets sold is 18.
System of linear equations
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of each type of ticket sold
In this case, let c be the number of child tickets and a be the number of adult tickets.
Each child ticket for a ride costs $2, while each adult ticket costs $6.
The ride collected a total of $148, and 38 tickets were sold.
So, the system of equations to be solved is
[tex]\left \{ {{c+a=38} \atop {2c+6a=148}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "c" from the first equation you get:
c=38 - a
Then, substituting the expression in the second equation you get:
2×(38 - a) +6a=148
Solving:
2×38 - 2a +6a=148
76 - 2a +6a=148
76 Â +4a=148
4a= 148 - 76
4a= 72
a= 72÷ 4
a=18
Now, replacing in the expression c=38 -a you get:
c= 38 -a
c= 38 - 18
c= 20
Finally, the number of child tickets sold is 20 and the number of adult tickets sold is 18.
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