can you help me solve this problem? use a system to solve it.?

Question

tickets to a localmovie were sold at $3.00 for adults and $1.50 for students. if 134 tickets were sold for a total of $351.00, how many adult tickets were sold?

Answer 1

Let a = adult tickets and s = student tickets. It is obvious that

a+s = 134, and
(3.00)a + (1.50)s = 351

Now we just have a system of equations with two unknowns.

Let's multiply the first equation by 3, to get

3a + 3s = 402
3a + (1.5)s =351

(Note, I just converted 3.00 into 3, to avoid redundancy).

Now, subtract the equations.

(3a + 3s) - (3a + 1.5s) = (402 - 351)
3s - 1.5s = 51
1.5s = 51
s = 34

We know that s = 34, but s is the # of student tickets so we want a. Fortunately, we have an equation for that.

a + s = 134

And we just substitute s = 34 to get a.
a + 34 = 134
a = 100

Therefore, 100 adult tickets were sold.

Answer 2

A = # of adult tickets
S = # of student tickets

1) A + S = 134

2) 300A + 150S = 35100
2A + S = 234 {divide by 150}

Solve equation 1 for A and substitute into equation 2

1) A = 134 - S

2) 2(134 - S) + S = 234
268 - 2S + S = 234
-S = -34
S = 34

A = 134 - 34
A = 100

Check

300A + 150S = 35100
300(100) + 150(34) = 35100
30000 + 5100 = 35100
35100 = 35100

Answer 3

YOur 2 equations are
3x + 1.5y = 351
x + y =134

Answer 4

a+c=134
c=134-a
3a+1.5c=351
3a+1.5(134-a)=351
1.5a+201=351
1.5a=150
a=100
c=134-a=134-100=34

100 adult tickets
34 child tickets

check
3*100+1.5*34=300+51=351