Question

John’s school is selling tickets to a fall musical. On the first day of the ticket sales the school sold 5 senior citizen tickets and 14 child tickets for a total of $102. The school took in $153 on the second day by selling 11 senior citizen tickets and 7 child tickets. What is the price of each senior citizen ticket & one child ticket?

Answer 1

Price of each senior citizen ticket is
`\$12` and one child ticket is
`\$3`

Explanation:

Let the price of each senior citizen ticket be x.

Let the price of each Child ticket be y.

Tickets sold on first day which are given as,

5 senior citizen tickets and 14 child tickets for a total of $102.

`5x+14y = \$ 102 \ \ equation \ 1`

Tickets sold on first day which are given as,

$153 on the second day by selling 11 senior citizen tickets and 7 child tickets.

`11x+7y= \$153 \ \ \ equation\ 2`

Now multiplying by 2 equation 2 we get

`2* (11x+7y)= 2 *\$153\\22x+14y = \$ 306 \ \ \ equation\ 3`

Now Subtracting equation 1 from equation 3 we get

`17x= 204\\x=(204)/(17) = \$12`

Substituting value of x in equation 1 we get

`5 *12+14y=\$102\\14y=\$102-42\\14y= \$42\\y=\$(42)/(14)=\$4`

Hence Senior Citizen ticket price is
`\$12` and Child ticket price is
`\$3`