a group of 9 people spent $78 to go to the movies.adult tickets cost$10 each and student tickets cost $8 each.How many adult tickets were purchased?
3 adult tickets
Thanks
6 Student tickets X $8.00 = $48.00
$78.00 minus the $48.00 = $30.00
$30.00 divided by $10.00 Adult Cost = 3 adult tickets.
To find the number of adult tickets that were purchased, we can use algebraic equations. Let's assume the number of adult tickets purchased is represented by the variable "A".
Given that there are 9 people in the group, the total number of tickets purchased can be represented by the equation: A (number of adult tickets) + S (number of student tickets) = 9 (total number of people).
We also know that the cost of adult tickets is $10 each, and the cost of student tickets is $8 each. So, the total cost of the tickets can be represented as another equation: 10A + 8S = 78.
Now we can solve the system of equations to find the value of A:
1. Multiply the first equation by 8 to make the coefficients of S the same in both equations: 8A + 8S = 72.
2. Subtract the modified first equation from the second equation: (10A + 8S) - (8A + 8S) = 78 - 72.
Simplifying: 2A = 6.
3. Divide both sides of the equation by 2: A = 3.
Therefore, 3 adult tickets were purchased.
Let x = adult tickets and y = student ones.
x = 9 - y
10x + 8y = 78
Substitute 9-y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.