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?
sorry my answers are 7 adults and 1 student
Hmmm. The problem says 9 people.
How do you justify your answer?
To solve this problem, we can set up a system of equations. Let's denote the number of adult tickets as 'A' and the number of student tickets as 'S'.
According to the problem, there are a total of 9 people, so we know that A + S = 9.
Additionally, we know that adult tickets cost $10 each and student tickets cost $8 each. Since the total amount spent was $78, we can also set up the equation: 10A + 8S = 78.
Now we have a system of equations:
A + S = 9
10A + 8S = 78
To solve this system, we can use the method of substitution or elimination. Let's use the substitution method.
Step 1: Solve the first equation for A:
A = 9 - S
Step 2: Substitute A in the second equation with 9 - S:
10(9 - S) + 8S = 78
Step 3: Simplify and solve for S:
90 - 10S + 8S = 78
-2S = 78 - 90
-2S = -12
S = -12 / -2
S = 6
Now that we know S = 6, we can substitute this value back into the first equation to find the value of A:
A + 6 = 9
A = 9 - 6
A = 3
Therefore, 3 adult tickets were purchased.