Answer:
If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.
Step-by-step explanation:
A system of linear equations is a set of linear equations that have more than one unknown, which are related through the equations.
In this case, being:
The system of equations is:
[tex]\left \{ {{83*A+42*C=874} \atop {102*A+67*C=1151}} \right.[/tex]
The substitution method consists of isolating one of the two unknowns in one equation to replace it in the other equation. In this case you isolate C from the first equation:
83*A + 42*C= 874
42*C= 874 - 83*A
[tex]C=\frac{874 - 83*A}{42}[/tex]
Substituting this expression in the second equation:
[tex]102*A + 67*\frac{874 - 83*A}{42}= 1151[/tex]
and solving:
[tex]102*A + \frac{67}{42} *(874 - 83*A)= 1151[/tex]
Multiply through by 42
[tex]42*102*A + 42*\frac{67}{42} *(874 - 83*A)= 42*1151[/tex]
4,284*A + 67*(874-83*A)= 48,342
4,284*A + 58,558 - 5,561*A= 48,342
4,284*A - 5,561*A= 48,342 - 58,558
-1,277*A= -10,216
[tex]A=\frac{-10,216}{-1,277}[/tex]
A= 8
Knowing that: [tex]C=\frac{874 - 83*A}{42}[/tex] then:
[tex]C=\frac{874 - 83*8}{42}[/tex]
[tex]C=\frac{874 - 664}{42}[/tex]
[tex]C=\frac{210}{42}[/tex]
C= 5
The price of an adult ticket is $8 and a child is $5. If 48 adults and 26 children attended the matinee on Sunday, then:
$8*48 adults + $5* 26 childen= $514
If 48 adults and 26 children attended the matinee on Sunday, the theater raised $ 514 from ticket sales.
