SOLUTION: We are working with solving multi-step equations with one variable. I need to write an equation to solve the following: The attendance at a baseball game was 400 people. Stude

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Question 911377: We are working with solving multi-step equations with one variable. I need to write an equation to solve the following:
The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total tickets sales were $1050. How many tickets of each type were sold?
I can't figure out what the equation should be using x to represent the number of tickets.

Found 2 solutions by richwmiller, MathTherapy:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
total sold 400
total sales 1050
product sold at 2 and 3
a+b=400,
2*a+3*b=1050
a=400-b
We have two equations with two variables.
We will substitute to make one equation with one variable
2*(400-b)+3*b=1050
800-2b+3*b=1050
1*b=250
b=250
a=400-b
a=150 at $2 and b=250 at $3
check
150+250=400
2*a+3*b=1050
2*150+3*250=1050
300+750=1050
1050=1050
ok
codetickv

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

We are working with solving multi-step equations with one variable. I need to write an equation to solve the following:
The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total tickets sales were $1050. How many tickets of each type were sold?
I can't figure out what the equation should be using x to represent the number of tickets.


Since 400 people attended, it's safe to assume that a total of 400 tickets were sold

Let the NUMBER of student tickets sold, be x

With 400 tickets being sold, and with x being the number of STUDENT tickets sold, the number of ADULT

tickets sold = 400 - x

With each student ticket costing $2, proceeds from the sale of student tickets = 2x

With each adult ticket costing $3, proceeds from the sale of adult tickets = 3(400 - x)

Now, since total proceeds from sales was $1,050, then we can say that:

2x + 3(400 - x) = 1,050

2x + 1,200 - 3x = 1,050

2x - 3x = 1,050 - 1,200

- x = - 150

x, or number of student tickets sold = , or 

You should be able determine the number of adult tickets that were sold 

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