The ticket prices for a movie are shown in the illustration. Receipts for one showing were $1,990 for an audience of 215 people. How many general admission tickets and how many senior citizen tickets were sold?
(General admission tickets: $10
Senior tickets: $6)
count the tickets: g+s = 215
count the dollars: 10g+6s = 1990
Now crank it out.
g = 215 - s
10g + 6s = 1990
Substitute 215-s for g in the second equation and solve for s. Insert that value into the first equation to solve for g. Check by putting both values into the second equation.
S= 40
g = 150
To find the number of general admission and senior citizen tickets sold, we need to set up a system of equations based on the given information.
Let's assume that the number of general admission tickets sold is represented by "G," and the number of senior citizen tickets sold is represented by "S."
According to the given information, the total receipts from selling the tickets were $1,990. We can use this information to set up our first equation:
10G + 6S = 1990
Additionally, we are told that the number of people in the audience was 215. So we can set up our second equation based on this information:
G + S = 215
Now we have a system of equations:
10G + 6S = 1990
G + S = 215
To solve this system, we can use the method of substitution or elimination.
Let's solve it using the elimination method:
Multiply the second equation by 6 to make the coefficients of G in both equations the same:
6(G + S) = 6(215)
This simplifies to:
6G + 6S = 1290
Now, we can subtract the second equation from the first equation:
(10G + 6S) - (6G + 6S) = 1990 - 1290
This simplifies to:
4G = 700
Dividing both sides of this equation by 4 gives us:
G = 175
Now, substitute this value of G back into either of the original equations. Let's substitute it into the second equation:
175 + S = 215
This simplifies to:
S = 215 - 175
S = 40
Therefore, 175 general admission tickets and 40 senior citizen tickets were sold.