how do you do this word problem you can use any system of equation to solve?

Question

tickets to local movie were sold at $4.00 for adults and $2.50 for students. if 267 tickets were sold for a total of $1042.50, how many adult tickets were sold?

Answer 1

These kinds of questions always follow the same pattern.

One equation will always be, how many tickets were sold of each type?

If s = # of student tickets and a = # of adult tickets, then:

s + a = 267

The other equation will always be, how much of the money collected was from student tickets, and how much from adult tickets?

The amount of money collected from student tickets is 2.50 x s.
The amount of money collected from adult tickets is 4 x a.
The total amount collected is $1042.50.

2.5s + 4a = 1042.50

Solve for a.

Answer 2

Say we have A adults and S students.
Then:
Total number of people is 267:
A+S = 267
Total cost is 1042.50:
4.00A + 2.50S = 1042.50
Multiplying the first equation by 4 gives:
4A + 4S = 1068.
Subtracting the second equation gives
1.5S = 25.5
So S = 17.
So using the first equation, A = 250.

Answer 3

Let there be a adult tickets

So there are (267 - a) students tickets

4a + 2.50 (267 - a) = 1042.50

1.50a + 667.50 = 1042.50.......subtract 667.50 from both sides,

1.50 a= 375

a = 375 x 2/3

a = 250

250 adults and 17 students

Answer 4

I will answer without using equations
a) Suppose all people were adults.
267 * 4,00 = $1068.00
b) They were sold 1068.00 - 1042.50 = $25.50 less (Why?)
c) Because there were students paying $1,50 Less than adults
d) So there were 25.50/1.50 = 17 students
267 (total) - 17(student) = 250 adults.

I answered this way just for fun : Always use equations

Answer 5

250 adult tickets x $4.00 = $1,000.00
17 kids tickets x $2.50 = 42.50

Answer 6

You would just multiply each one until you got a number that would fit into the given answer. Sort of like trial and error.

Answer 7

wouldn't u divide?