Question

Five family members went to a carnival.

-They spent a total of $31.00 for tickets.
-Students tickets cost $5.00
-Adult tickets cost $7.00 each.

Write and solve a system of equations to determine how many adult tickets were purchased.

Answer 1

$31.00 -------------------------------->for tickets.

Students tickets (A) cost ----------->$5.00
Adult tickets (B) ----------------------->cost $7.00
x-> numbers of tickets Students
y-> numbers of tickets Adult
x+y=5----------x=5-y
5x+7y=31
resolving
5(5-y)+7y=31--------------25-5y+7y=31
y=3
therefore x=2

Answer 2

Answer:
number of adult tickets = 3 tickets
number of student tickets = 2 tickets

Step-by-step explanation:
Assume that the number of adult tickets is x and the number of students tickets is y.
Now, we are given that:
1- The number of members is 5. This means that they bought a total of 5 tickets.
This can be written as:
x + y = 5
Which can be rewritten as:
x = 5-y ........> equation I
2- They spent a total of $31.00 for tickets.
-Students tickets cost $5.00
-Adult tickets cost $7.00 each.
This means that:
7x + 5y = 31 ......> equation II

Substitute with equation I in equation II to get y as follows:
7x + 5y = 31
7(5-y) + 5y = 31
35 - 7y + 5y = 31
35-31 = 7y - 5y
4 = 2y
y = 2

Substitute with the y in equation I to get the x as follows:
x = 5 - y
x = 5 - 2
x = 3

Based on the above:
number of adult tickets = x = 3 tickets
number of student tickets = y = 2 tickets

Hope this helps :)