Taking into account the definition of a system of linear equations, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
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.
In this case, a system of linear equations must be proposed taking into account that
Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets sold.
So, the system of equations to be solved is
[tex]\left \{ {{3x+5y=2820} \atop {x=3y+30}} \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, substituting the second equation in the first you get:
3×(3y+30)+5y=2820
Solving:
3×3y+3×30+5y=2820
9y+90+5y=2820
9y+5y=2820 - 90
14y= 2730
y= 2730÷ 14
y= 195
Remembering that x=3y +30, then:
x= 3×195 + 30
Solving
x=585 +30
x=615
Finally, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
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