Answer:
Student ticket=$10. Senior ticket=$7
Step-by-step explanation:
If we say Student ticket price = Y. and senior ticket price = X. Then we can say:
[tex]3x+5y=71\\10x+12y=190[/tex]
We can rewrite one of the equations as y equals:
[tex]10x=190-12y[/tex]
Then, we simply solve for x.
[tex]\frac{10x=190-12y}{10}=x=19-1.2y[/tex]
Then, we use the other equation and replace x with the equation we just solved
[tex]3(19-1.2y)+5y=71\\[/tex]
We simplify and it becomes:
[tex]57-3.6y+5y=71[/tex]
Then we subtract 57 from each side and get:
[tex]-3.6y+5y=-14[/tex]
Next, we combine the y and get:
[tex]1.4y=14[/tex]
Then we divide by 1.4 and get:
[tex]\frac{1.4y=14}{1.4} =y=10[/tex]
This means that the cost per student ticket is $10
Next we replace the y value in an equation with 10 and solve:
[tex]3x+5y=71\\3x+5(10)=71\\3x+50=71\\[/tex]
Then we subtract 50 from each side:
[tex]3x+50=71\\-50\\3x=21[/tex]
Finally, we divide each side by 3:
[tex]\frac{3x=21}{3} =x=7[/tex]
This means that each senior ticket costs $7
