Ok, This is the question:
The attendance at a baseball game was 400 people. Student Ticket cost $2 and adult tickets cost were $3. Total Ticket Sales were $1050. How many tickets of each type were sold?
This is what I did:
2x+400=1050
-400=-400
-----------
2x=650
x=325
3y+400=1050
-400=-400
-----------
3y=650
y=216.6=217
Two people told me its wrong...
One said to do this:
2x + 3(400-x)=1050
I don't really know how to break this down.
And, another person said:
If S is the number of students and A is the number of adults,
S + A = 400
2S + 3A =1050
2S + 2A = 800
Subtract the last equation from the one above. That will give you what A is. S is 400 -A
I don't really understand how the person got 800.
Is it like this?
2(S+A)=400
2S+SA=800
Is this right? If so, what do I do after this? I'm really confused. Help will be greatly appreciated.
S=150 and A=250
S+A=400
A=400-S
2S+3(400-S)=1050
Solve for S
S=150
Plug back in top equation
A=250
To solve this problem, let's break it down step by step:
1. Let's define the variables:
Let S be the number of student tickets sold.
Let A be the number of adult tickets sold.
2. Based on the given information, we can set up two equations:
Equation 1: S + A = 400 (since the total attendance is 400 people)
Equation 2: 2S + 3A = 1050 (since the total ticket sales amount to $1050)
Now we have a system of equations that we can solve simultaneously.
3. One approach is to solve equation 1 for S (in terms of A) and substitute it into equation 2:
Equation 1: S = 400 - A
Substituting this value of S into equation 2:
2(400 - A) + 3A = 1050
800 - 2A + 3A = 1050
800 + A = 1050
A = 250
4. Now that we have the value of A, we can substitute it back into equation 1 to find the value of S:
S + 250 = 400
S = 150
Therefore, 150 student tickets and 250 adult tickets were sold.
Regarding the alternative approaches you mentioned:
- The first approach you mentioned is correct. It sets up an equation with two variables (x and 400-x) representing the number of student and adult tickets sold respectively. However, it seems that you may have made an error in your calculation.
- The second approach you mentioned is also correct. It sets up two equations based on the given information. The equation 2S + 2A = 800 is derived from multiplying the first equation (S + A = 400) by 2. Subtracting this equation from equation 2 (2S + 3A = 1050) eliminates the variable S, allowing you to solve for A.
I hope this explanation clarifies the solution process. Let me know if you have any further questions!