Miguel sells 77 to a barbeque, for a total of $443. If the tickets cost $7.00 for adults and $5.00 for children, how many of each ticket did he sell?
Let x = adult's tickets and y = children's tickets
x + y = 77
Therefore, x = 77 - y
7x + 5y = 443
Substitute 77 - y for x in the second equation and solve for y. Put value into first equation to find x. Check by putting both into the second equation.
I hope this helps.
To solve this problem, let's define the variables:
Let's say the number of adult tickets sold is "A".
Let's say the number of child tickets sold is "C".
According to the problem, Miguel sold 77 tickets in total. So we can write the first equation:
Equation 1: A + C = 77
The total revenue from selling the tickets was $443. The price of an adult ticket is $7.00, and the price of a child ticket is $5.00. So we can write the second equation:
Equation 2: 7A + 5C = 443
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (A and C). We can solve this system of equations to find the values of A and C.
There are a few ways to solve this system of equations, such as substitution, elimination, or graphing. Let's use the substitution method.
From Equation 1, we can solve for A in terms of C:
A = 77 - C
Substitute this expression for A in Equation 2:
7(77 - C) + 5C = 443
Now we can solve for C:
539 - 7C + 5C = 443
-2C = 443 - 539
-2C = -96
C = (-96)/(-2)
C = 48
Now substitute the value of C back into Equation 1 to find A:
A = 77 - 48
A = 29
So, Miguel sold 29 adult tickets and 48 child tickets.