how do u solve the follow question? you are selling tickets to a football game. Student tickets (x) cost $4 and general admission tickets (y) cost $7. You sell 26 tickets and collect $140. How many of each type of ticket did u sell?
x + y = 26 The number of tickets
4x + 7y = 140 The value of the tickets.
Multiply the first equation by -4 and then add the two equations together. Solve for y. You can then use the original first equation to solve for x.
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To solve this question, you can set up a system of equations based on the given information. Let's assign variables to the unknown quantities:
Let x be the number of student tickets sold.
Let y be the number of general admission tickets sold.
From the problem statement, we can derive two equations:
1) The total number of tickets sold: x + y = 26
2) The total amount collected from the ticket sales: 4x + 7y = 140
Now, we have a system of two equations with two unknowns. We can solve this system to find the values of x and y.
There are several methods to solve a system of equations, such as substitution, elimination, or using matrices. Let's solve this system using the substitution method:
From equation 1, we can express x in terms of y by subtracting y from both sides:
x = 26 - y
Now, substitute this expression for x in equation 2:
4(26 - y) + 7y = 140
Simplify and solve for y:
104 - 4y + 7y = 140
3y = 140 - 104
3y = 36
y = 36 / 3
y = 12
We have found that y, the number of general admission tickets sold, is 12.
Now, substitute this value of y back into equation 1 to find x:
x + 12 = 26
x = 26 - 12
x = 14
Therefore, the number of student tickets sold, x, is 14.
In conclusion, you sold 14 student tickets and 12 general admission tickets.