The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold f or one showing with a total revenue of $1010. If the number of adult tickets sold was 10 less than twice the number of teacher tickets, how many of each
type of ticket were sold for the showing?
Define the variables for this situation. Use the variables a, t, and s.
1 answer:
Answer:
adults, a = 116
Students, s = 111
Teacher, t = 53
Step-by-step explanation:
Adult = $6
Teacher = $4
Students = $2
Let
Adults = a
Teacher = t
Students = s
Total revenue = $1010
Total tickets sold = 280
a = 2t - 10
a + s + t = 280
6a + 2s + 4t = 1010
Substitute a = 2t - 10 into the equation
2t - 10 + s + t = 280
6(2t - 10) + 2s + 4t = 1010
3t + s - 10 = 280
12t - 60 + 2s + 4t = 1010
3t + s = 280 + 10
16t + 2s = 1010 + 60
3t + s = 270 (1)
16t + 2s = 1070 (2)
Multiply (1) by 2
6t + 2s = 540 (3)
16t + 2s = 1070 (4)
Subtract (3) from (4)
16t - 6t = 1070 - 540
10t = 530
Divide both sides by 10
t = 530/10
= 53
t = 53
Substitute t =53 into (1)
3t + s = 270
3(53) + s = 270
159 + s = 270
s = 270 - 159
= 111
s = 111
Substitute the values of s = 111 and t = 53 into
a + s + t = 280
a + 111 + 53 = 280
a + 164 = 280
a = 280 - 164
= 116
adults, a = 116
Students, s = 111
Teacher, t = 53
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Have a good day Ma'am/Sir.
2.75 inches. 5x11 is 55 so .25x11 is 2.75
Okay here we go! 56.6-3.2=53.4divide that by 2 is 26.7-another 6 so we have 20.7 ml of the solution left hope this helped