de Sean it in school is selling tickets to a choral performance. on the first day of ticket selling the school sold eight senior citizen tickets and 12 students tickets for a total of $160. The school took in 115 on the second day by selling 11 senior citizen tickets and six student tickets. find the price of a senior cytisine take it in the price of a student ticket.
price of senior ticket --- x
price of student tickets -- y
day 1:
8x + 12y = 160
day 2:
11x + 6y = 115
day 1 equation ÷ 2
4x + 6y = 80
subtract from day 2 equation:
11x + 6y = 115
4x + 6y = 80
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7x = 35
x = 5
back in 4x+6y = 80
20 + 6y = 80
6y = 60
y =10
Seniors cost $5.00 and students cost $10.00
To find the price of a senior citizen ticket and the price of a student ticket, we can set up a system of equations based on the given information.
Let's use the variables:
S = price of a senior citizen ticket
C = price of a student ticket
Based on the first day sales, we know that:
8S + 12C = 160 (equation 1)
Based on the second day sales, we know that:
11S + 6C = 115 (equation 2)
We now have a system of equations. We can solve this system using various methods, such as substitution or elimination.
Using the substitution method, we can solve equation 1 for S and then substitute it into equation 2.
From equation 1, we can isolate S:
8S = 160 - 12C
S = (160 - 12C) / 8
Now substitute this value of S into equation 2 and solve for C:
11((160 - 12C) / 8) + 6C = 115
Multiply through by 8 to get rid of the denominator:
11(160 - 12C) + 48C = 920
Distribute and simplify:
1760 - 132C + 48C = 920
-84C = 920 - 1760
-84C = -840
C = -840 / -84
C = 10
Now substitute the value of C back into equation 1 to find S:
8S + 12(10) = 160
8S + 120 = 160
8S = 160 - 120
8S = 40
S = 40 / 8
S = 5
Therefore, the price of a senior citizen ticket is $5, and the price of a student ticket is $10.