Question

The school that Imani goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets and 3 child tickets for a total of $69. The school took in $91 on the second day by selling 5 senior citizen tickets and 3 child tickets. What is the price each of one senior citizen ticket and one child ticket?​

Answer 1

Answer:

Cost of one senior citizen ticket = $11

Cost of one child ticket = $12

Step-by-step explanation:

Let,

x be the cost of one senior citizen ticket

y be the cost of one child ticket

According to given statement;

3x + 3y = 69      Eqn 1

5x + 3y = 91      Eqn 2

Subtracting Eqn 1 from Eqn 2

(5x+3y)-(3x+3y) = 91 - 69

5x+3y-3x-3y = 22

2x = 22

Dividing both sides by 2

$\frac{2x}{2}=\frac{22}{2}$

x = 11

Putting x = 11 in Eqn 1

3(11) + 3y = 69

33 + 3y = 69

3y = 69 - 33

3y = 36

Dividing both sides by 3

$\frac{3y}{3}=\frac{36}{3}\\y=12$

Hence,

Cost of one senior citizen ticket = $11

Cost of one child ticket = $12