movie tickets cost $10 for adults and $8 for children. The total sales form 120 tickets was $1120. how many adult tickets were sold?
A + C = 120
10 A + 8 C = 1120
Solve that pair of equations for the two unknowns
C = 120 - A
10 A + 960 -8A = 1120
2A = 160
A = 80
C = 40
To solve this problem, we need to set up a system of equations. Let's denote the number of adult tickets as "a", and the number of children's tickets as "c".
1. The first equation represents the total number of tickets sold: a + c = 120.
2. The second equation represents the total sales from the tickets: 10a + 8c = 1120.
Now, we can solve the system of equations to find the value of "a" (the number of adult tickets).
One approach is to solve the first equation for one variable (a or c), substitute it into the second equation, and solve for the other variable.
From the first equation, we can express "a" in terms of "c" as a = 120 - c.
Substitute this value of "a" into the second equation, we get: 10(120 - c) + 8c = 1120.
Simplifying the equation: 1200 - 10c + 8c = 1120.
Combine like terms: -2c = 1120 - 1200.
Simplifying further: -2c = -80.
Divide both sides of the equation by -2: c = -80 / -2 = 40.
By substituting back into the first equation, a + 40 = 120, we find that a = 80.
Therefore, 80 adult tickets were sold.
Alternatively, we can solve the system of equations using the elimination method or substitution method. Each method is a valid way to find the solution, and the choice depends on personal preference or familiarity.