Respuesta :
Let x be the number of adults that went to the game, and y be the number of children, since the number of total of people that went to the game is 166, then:
[tex]x+y=166.[/tex]Now, each adult ticket had a cost of $2.10, each child's ticket had a cost of $0.75, and the total amount taken in was $293.25. Therefore:
[tex]2.10x+0.75y=293.25.[/tex]Solving the first equation for x we get:
[tex]x=166-y\text{.}[/tex]Substituting the above equation in the second equation and solving for y we get:
[tex]\begin{gathered} 2.10\cdot(166-y)+0.75y=293.25, \\ 348.6-2.10y+0.75y=293.25, \\ -1.35y=-55.35, \\ y=41. \end{gathered}[/tex]Substituting y=41 in the third equation on the board we get:
[tex]\begin{gathered} x=166-41, \\ x=125. \end{gathered}[/tex]Answer:
The system of equations is:
[tex]\begin{gathered} x+y=166, \\ 2.10x+0.75y=293.25. \end{gathered}[/tex]Where x is the number of adults that went to the game and y is the number of children.
The number of adults that attended is 125 and the number of children is 41.
