You are buying tickets for a concert. Adult tickets cost $12 each, and child tickets cost $6 each. You buy a total of 8 tickets and spend $72. How many adult and child tickets did you buy?
Let's say you bought x adult tickets.
The cost of x adult tickets is $12*x = $<<12*x=12x>>12x.
The cost of (8 - x) child tickets is (8 - x) * $6 = $48 - $6x.
The total cost of the tickets is $72.
So, 12x + 48 - 6x = 72.
Combining like terms, we get 6x + 48 = 72.
Subtracting 48 from both sides, we get 6x = 24.
Dividing both sides by 6, we get x = 4.
So, you bought 4 adult tickets and 8 - 4 = <<8-4=4>>4 child tickets. Answer: \boxed{4}.
Let's assume you bought x adult tickets and y child tickets.
According to the given information, adult tickets cost $12 each, so the total cost of adult tickets would be 12x dollars.
Child tickets cost $6 each, so the total cost of child tickets would be 6y dollars.
The total number of tickets you bought is 8, so we can write the equation:
x + y = 8
You spent a total of $72, so we can write another equation:
12x + 6y = 72
We can solve this system of equations to find the values of x and y. Let's solve it using the substitution method.
From the first equation, we can solve for x in terms of y, as follows:
x = 8 - y
Now, substitute this value of x in the second equation:
12(8 - y) + 6y = 72
96 - 12y + 6y = 72
96 - 6y = 72
-6y = 72 - 96
-6y = -24
y = -24 / -6
y = 4
Now substitute the value of y in the first equation to find x:
x + 4 = 8
x = 8 - 4
x = 4
Therefore, you bought 4 adult tickets and 4 child tickets.
To solve this problem, let's assign variables to the unknown quantities. Let's say the number of adult tickets you bought is 'a', and the number of child tickets you bought is 'c'.
Now, let's write two equations to represent the information given in the problem:
1) The total number of tickets bought: a + c = 8
2) The total cost of the tickets: 12a + 6c = 72
We have a system of two equations with two unknowns. To solve this system, we can use the method of substitution or elimination.
Let's solve it using the substitution method:
From equation 1, we can express 'a' in terms of 'c': a = 8 - c
Now, substitute this value of 'a' into equation 2:
12(8 - c) + 6c = 72
96 - 12c + 6c = 72
96 - 6c = 72
-6c = 72 - 96
-6c = -24
c = (-24)/(-6)
c = 4
Now that we know 'c', substitute this value back into equation 1 to find 'a':
a + 4 = 8
a = 8 - 4
a = 4
Therefore, you bought 4 adult tickets and 4 child tickets.