A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. An adult ticket costs as much as the combined cost of a student ticket and a child ticket. you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23. what are 3 system of equations? what is the price per ticket for each type of ticket?

Answer:The price per ticket for adults is $5The price per ticket for students is $4The price per ticket for child between the ages of 3 and 8  is $1Step-by-step explanation:Letx -----> the price per ticket for adults y -----> the price per ticket for studentsz -----> the price per ticket for child between the ages of 3 and 8 we know thatThe system of equations is[tex]2x+y+z=15[/tex] ------> equation A[tex]x=y+z[/tex] ------> equation B[tex]x+4y+2z=23[/tex] -----> equation Csubstitute equation B in equation A and solve for x[tex]2x+(x)=15[/tex][tex]3x=15[/tex][tex]x=5[/tex]Substitute the value of x in equation B and equation C[tex]5=y+z[/tex] -----> equation B[tex]5+4y+2z=23[/tex][tex]4y+2z=18[/tex] -----> equation CSolve the system by graphingRemember that the solution is the intersection point both graphsUsing a graphing toolThe solution is the point (1,4)soz=1, y=4thereforeThe price per ticket for adults is $5The price per ticket for students is $4The price per ticket for child between the ages of 3 and 8  is $1