student tickets to the school musical cost $3 each. All other tickets cost $5 each. Suppose that 272 tickets were sold for a total of $1120. How many tickets of each type were sold?
x = student tickets
y = "other" tickets
x + y = 272
3x + 5y = 1120
Solve those equations..
3x + 3y = 816
2y = 304
y = 152
x = 120
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To solve this problem, we can set up a system of equations based on the given information. Let's call the number of student tickets sold as 's' and the number of other tickets sold as 'o'.
We are given three pieces of information:
1. The cost of student tickets is $3 each.
2. The cost of all other tickets is $5 each.
3. A total of 272 tickets were sold, and the total revenue was $1120.
Based on this information, we can write two equations:
1. The total number of tickets sold: s + o = 272
2. The total revenue generated: 3s + 5o = 1120
Now, we have a system of equations:
s + o = 272 ...(equation 1)
3s + 5o = 1120 ...(equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From equation 1, we can write s = 272 - o.
Now substitute this value of s into equation 2:
3(272 - o) + 5o = 1120
816 - 3o + 5o = 1120
816 + 2o = 1120
2o = 1120 - 816
2o = 304
o = 304/2
o = 152
Therefore, the number of other tickets sold (o) is 152. Now, substitute this value into equation 1 to find the number of student tickets sold (s):
s + 152 = 272
s = 272 - 152
s = 120
So, the number of student tickets sold (s) is 120.
In summary:
The number of student tickets sold is 120, and the number of other tickets sold is 152.