Answer :
Answer:
The price of 1 senior citizen ticket is $4
The price of 1 adult ticket is $7
The price of 1 child ticket is $5
Step-by-step explanation:
Assume that the costs of a senior ticket is $x , an adult ticket is $y and
a child ticket is $z
First day:
The school sold 4 senior citizen tickets, 2 adult tickets and 5 child
tickets for a total of $55
∴ 4x + 2y + 5z = 55 ⇒ (1)
Second day:
The school sold 7 senior citizen tickets, 2 adult tickets and 5 child
tickets for $67
∴ 7x + 2y + 5z = 67 ⇒ (2)
Third day:
The school sold 2 senior citizen tickets, 4 adult tickets and 2 child
tickets for $46
∴ 2x + 4y + 2z = 46 ⇒ (3)
The number of adult tickets and the number of child tickets in the first
and second days are equal, then we can subtract equation (1) from
equation (2) to find x
Subtract equation (1) from equation (2)
∴ (7x - 4x) + (2y - 2y) + (5z - 5z) = 67 - 55
∴ 3x = 12
Divide both sides by 3
∴ x = 4
Substitute the value of x in equation (2)
∴ 7(4) + 2y + 5z = 67
∴ 28 + 2y + 5z = 67
Subtract 28 from both sides
∴ 2y + 5z = 39 ⇒ (4)
Substitute the value of x in equation (3)
∴ 2(4) + 4y + 2z = 46
∴ 8 + 4y + 2z = 46
Subtract 8 from both sides
∴ 4y + 2z = 38 ⇒ (5)
Now lets solve equations (4) and (5) to find y and z
Multiply equation (4) by -2 to eliminate y
∴ -4y - 10z = -78 ⇒ (6)
Add equations (5) and (6)
∴ -8z = -40
Divide both sides by -8
∴ z = 5
Substitute the value of z in equation (4) or (5)
∴ 2y + 5(5) = 39
∴ 2y + 25 = 39
Subtract 25 from both sides
∴ 2y = 14
Divide both sides by 2
∴ y = 7
The price of 1 senior citizen ticket is $4
The price of 1 adult ticket is $7
The price of 1 child ticket is $5