Answer:
404 tickets to adults have been sold .
325 tickets to students have been sold .
Step-by-step explanation:
A system of linear equations is a set of two or more first degree equations, in which two or more variables are related.
In this case, a system of two linear equations with two unknowns is solved.
To assemble the system of equations you must first define the variables, which in this case will be:
On the one hand, you know that 729 tickets were sold, that is to say that tickets sold for students and adults must add 729. Expressed in an equation this is: x+y=729 equation (A)
On the other hand, you know that during a game, $ 2995 was raised for the sale of those 729 tickets. And you also know that tickets for a high school football game cost $ 3 for students and $ 5 for adults.
Then the proceeds from the sale of tickets for students is 3*x and for adults it is 5*y. And your sum must be $ 2995. Expressed in an equation this is:
3*x + 5*y=2995 Equation (B)
So the system of equations is:
[tex]\left \{ {{x+y=729} \atop {3*x+5*y=2995}} \right.[/tex]
There are several methods of solving a system of equations. In that case, the substitution method will be used, which consists of isolating an unknown element in one of the equations, which will be a function of the other unknown. In the other equation that has not been used, the same unknown is replaced by the expression previously obtained. In this case, the value of variable x in equation (A) will be isolated:
x+y=729 ⇒ x=729-y Equation (C)
Replacing this expression in equation (B) you get:
3*(729-y)+5*y=2995
Solving this equation:
3*729-3*y+5*y=2995
2187+2*y=2995
2*y=2995-2187
2*y=808
y=808÷2
y=404
Remembering that "y" is tickets for admission to a high school football game for adults. this indicates that 404 tickets to adults have been sold .
Replacing this value in equation (C), which is the previously isolated equation, you get:
x=729-y
x=729-404
x=325
Remembering that "x" is tickets for admission to a high school football game for students. this indicates that 325 tickets to students have been sold .
