Question

Kathryns school is selling tickets to the annual dance competition on the first day of tickets sells the school sold for one senior citizen ticket and four child ticketsFor a total of $27 the school took in $82 on the second day by selling six senior citizen tickets and eight child tickets what is the price each of one senior citizen ticket and one child ticket

Answer 1

Each senior citizen ticket costs $7 and each child ticket costs $5.

Explanation:

Let,

x be the price of each senior citizen ticket

y be the price of each child ticket

According to given statement,

x+4y=27 Eqn 1

6x+8y=82 Eqn 2

Multiplying Eqn 1 by 2

2(x+4y=27)

2x+8y=54 Eqn 3

Subtracting Eqn 3 from Eqn 2

(6x+8y)-(2x+8y)=82-54

6x+8y-2x-8y=28

4x=28

Dividing both sides by 4

`(4x)/(4)=(28)/(4)\\x=7`

Putting x=7 in Eqn 1

7+4y=27

4y=27-7

4y=20

Dividing both sides by 4

`(4y)/(4)=(20)/(4)\\y=5`

Hence,

Each senior citizen ticket costs $7 and each child ticket costs $5.