Tickets for a concert cost $2 for children, $3 for students, and $4 for adults. Ticket sales totaled $522 and 177 people attende d the concert. Twice as many students as adults attended. Find how many of each type of ticket were sold. Assume that everyone who bought a ticket attended the concert.
1 answer:
Answer:
Children = 51
Adults = 42
Students= 84
Step-by-step explanation:
Children = $2
Students = $3
Adults = $4
Total sales = $522
Total people who attended = 177
Adults =a
Students = s= 2a
Children = c
c+s+a = 177 (1)
2c+3s+4a=522 (2)
Substitute s=2a into the equations
c + 2a + a = 177
c + 3a = 177 (3)
2c + 3(2a) + 4a = 522
2c + 6a + 4a = 522
2c + 10a = 522 (4)
c + 3a = 177 (3)
2c + 10a = 522 (4)
Multiply (3) by 2
2c + 6a = 354 (3b)
2c + 10a = 522
Subtract (3b) from (4)
10a - 6a = 522 - 354
4a = 168
Divide both sides by 4
a= 168/4
= 42
a= 42
s= 2a
= 2(42)
= 84
s= 84
Substitute the value of s and a into (1)
c+s+a = 177 (1)
c + 84 + 42 = 177
c + 126 = 177
c = 177 - 126
= 51
c=51
Children = 51
Adults = 42
Students= 84
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