Question

18) The school that John goes to is selling tickets to the annual talent show. On the first day of ticket

sales the school sold 3 senior citizen tickets and 5 student tickets for a total of $71. The school
took in $190 on the second day by selling 10 senior citizen tickets and 12 student tickets. Find
the price of a senior citizen ticket and the price of a student ticket.

Answer 1

Student ticket=$10. Senior ticket=$7

Explanation:

If we say Student ticket price = Y. and senior ticket price = X. Then we can say:

`3x+5y=71\\10x+12y=190`

We can rewrite one of the equations as y equals:

`10x=190-12y`

Then, we simply solve for x.

`(10x=190-12y)/(10)=x=19-1.2y`

Then, we use the other equation and replace x with the equation we just solved

`3(19-1.2y)+5y=71\\`

We simplify and it becomes:

`57-3.6y+5y=71`

Then we subtract 57 from each side and get:

`-3.6y+5y=-14`

Next, we combine the y and get:

`1.4y=14`

Then we divide by 1.4 and get:

`(1.4y=14)/(1.4) =y=10`

This means that the cost per student ticket is $10

Next we replace the y value in an equation with 10 and solve:

`3x+5y=71\\3x+5(10)=71\\3x+50=71\\`

Then we subtract 50 from each side:

`3x+50=71\\-50\\3x=21`

Finally, we divide each side by 3:

`(3x=21)/(3) =x=7`

This means that each senior ticket costs $7