# equation to model a story problem

#### cheymamma

##### New member
I need to write an equation to model the situation and then also solve the equation.

The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost$3. Total ticket sales were $1050. How many tickets of each type were sold? #### Subhotosh Khan ##### Super Moderator Staff member cheymamma said: I need to write an equation to model the situation and then also solve the equation. The attendance at a baseball game was 400 people. Student tickets cost$2 and adult tickets cost $3. Total ticket sales were$1050. How many tickets of each type were sold?
What are you supposed to find? ? How many tickets of each type were sold

Define your unknown variables (whose values you need to find):

# of students ticket = S

# of adult ticket = A

Please show us your work, idicating exactly where you are stuck - so that we may know where to begin to help you.

#### cheymamma

##### New member
Yes, how many ticket of each type were sold. And to write the equation. I am trying to help my daughter and I was never good at algebra.

#### Denis

##### Senior Member
Would be better/easier if your daughter was the one we dealt with.

#### cheymamma

##### New member
Well here she is, her name is Chey.

#### mmm4444bot

##### Super Moderator
Staff member

Here's an example exercise to study.

Some students and adults went to the movies. There were 15 people in this group.

Adult tickets cost $9, and student tickets cost$4.

The fifteen tickets for this group cost $85 total. How many adults went? How many students went? We begin by assigning symbols to represent the two unknown numbers that we've been asked to find. Let A = the number of adults Let S = the number of students The expression 9A represents the cost of all the adult tickets, yes? I mean, if we purchase A tickets and each one costs$9, then we multiply the number A times 9 to calculate the total cost.

Likewise, the expression 4S represents the cost of all the student tickets.

We know that these two dollar amounts (9A and 4S) add up to $85 total. These facts give us our first equation. 9A + 4S = 85 We can write another equation because we're also given the total number of tickets: 15 A + S = 15 These two equations containing the symbols A and S form what's called a "system of two equations with two unknowns". We can solve this system of equations using "the substitution method". (There are other methods, too.) The strategy of the substitution method is to write one symbol in terms of the other, and then substitute that expression. Doing this yields one equation with only one symbol. I'll choose to solve for A in terms of S. A + S = 15 Subtract S from both sides A = 15 - S Now we have a new expression for the number of adult tickets: 15 - S Hopefully, this expression makes sense, to you. It simply says that the number of adults is the difference between the total number of people and the number of students. We substitute this new expression for A into the other equation in the system. 9A + 4S = 85 9(15 - S) + 4S = 85 Now we have an equation that contains only the symbol S. We can solve for S in the usual way. 135 - 9S + 4S = 85 135 - 5S = 85 135 - 85 = 5S 50 = 5S 10 = S The group has 10 students. To find the number of adults, we go back to our formula above for A in terms of S. A = 15 - S A = 15 - 10 A = 5 The group has 5 adults. Lastly, we check our solution. Do 10 students and 5 adults add up to the given 15 people ? Do 10 tickets at$4 each plus 5 tickets at $9 each total the given$85 ?

Since the answer to both of these questions is yes, our answer checks.

Your posted exercise can be solved using the very same strategy.

I welcome specific questions. Please show any work that you can, if you would like more help.

Cheers ~ Mark