Question

There are 150 tickets sold for the school play. Tickets for students were $2 each and tickets for adults were $3 each. The total amount of money collected was $340. How many of each type of ticket were sold?

Answer 1

Answer: 40 adult tickets and 110 student tickets

There are two equations we’re going to make for this. The first is saying what the tickets are composed of. This is adult and students tickets. Let’s create this equation now.

150=s+a

The a represents the adult tickets, and the s is the student tickets.

Now let’s make an equation with the money. The $340 includes the 3a and 2s. Let’s make this equation now

340=2s+3a

Now let’s solve. The first equation 150=s+a is the same as writing a=150-s. Let’s substitute that in for a.

340=2s+3(150-s)

Now we can solve

340=2s+3(150-s)

*distribute*

340=2s+450-3s

*combine like terms*

340=-s+450

*subtract 450 on both sides*

340=-s+450
-450 -450
__________
-110=-s

*multiply by -1*

110=s

We now know that there are 110 student tickets. Let’s substitute this into the first equation to find the adult tickets.

150=a+s

150=a+110

Now let’s solve this

150=a+110

*subtract 110 on both sides*

150=a+110
-110 -110
________
40=a

Now we know that there were 40 adult tickets and 110 student tickets! Hope this helps comment below for more questions :)

Answer 2

Answer:the number of student tickets sold is 110

the number of adult tickets sold is 40

Explanation:

Let x represent the number of student tickets sold.

Let y represent the number of adult tickets sold.

There are 150 tickets sold for the school play. This means that

x + y = 150

Tickets for students were $2 each and tickets for adults were $3 each. The total amount of money collected was $340. This means that

2x + 3y = 340 - - - - - - - - - 1

Substituting x = 150 - y into equation 1, it becomes

2(150 - y) + 3y = 340

300 - 2y + 3y = 340

- 2y + 3y = 340 - 300

y = 40

Substituting y = 40 into x = 150 - y, it becomes

x = 150 - 40 = 110