The admission for a school play is $2.50 for children and $9.00 for adults. On a certain day, 288 people attended the play, and the total money collected from sales was $1760. How many children and how many adults were admitted?
adults ---- a
children --- 288 - a
solve for a:
9a + 2.5(288-a) = 1760
To solve this problem, we can use a method called "system of equations" by setting up two equations and solving them simultaneously.
Let's assume that the number of children attending the play is represented by the variable "C" and the number of adults attending is represented by the variable "A."
We can set up the following two equations based on the given information:
Equation 1: C + A = 288 (Total number of people attending the play is 288)
Equation 2: 2.50C + 9A = 1760 (Total money collected from sales is $1760)
Now, we can solve these equations to find the values of C and A.
We can start by solving Equation 1 for C:
C = 288 - A
Now, substitute this value of C in Equation 2:
2.50(288 - A) + 9A = 1760
Simplify and solve for A:
720 - 2.50A + 9A = 1760
6.50A = 1760 - 720
6.50A = 1040
A = 1040 / 6.50
A = 160
Now, substitute the value of A back into Equation 1 to find C:
C + 160 = 288
C = 288 - 160
C = 128
So, there were 128 children and 160 adults admitted to the school play.