Question

Brenda's school is selling tickets to a spring musical. On the first day of ticket sales, the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. Write the two constraints or equations for this problem.

Answer 1

Answer: The two constraints or equations for this problem are

3x + 9y = 75---- equation 1

8x + 5y =67------- Equation 2

can also be written as

x + 3y = 25 ----equation- 3

8x + 5y =67----- Equation 4

Which upon solving gave

x as cost of senior citizen = $4 and Y as cost of child ticket = $7

Explanation:

Step 1

Let the number of Senior citizen tickets be represented as x

let the number of child's tickets

be represented as y

Step 2 writing out the two equations for each day:

3x + 9y = 75---- equation 1

8x + 5y =67------- Equation 2

Step 3--Solving -------------

3x + 9y = 75 can also be written as

x + 3y = 25 when divide all by 3

Giving us

x + 3y = 25 ----- eqn 3

8x + 5y =67----- eqn 4

Multiplying eqn 3 by 8 and subtracting eqn 4

8x + 24y = 200

8x + 5y = 67

19y = 200-67

19y =133

y = 133/19 = 7

To get x

x +3y= 25

x = 25- 3(7)

x = 25-21

x = 4

x cost of senior citizen = $4 and Y cost of child ticket = $7