Can you tell me how to solve this math problem?

Question

Adult tickets for the senior class play cost $5 each and student tickets cost $3. A total of 1060 tickets costing $4500 were sold. How many student tickets were sold? Let t represent the number of student tickets sold.

I know that the answer is 400. I just don't know how to get the answer.

Please help! Thanks. =)

Answer 1

So with the info provided in this question, the number of adult tickets sold would be 1060-t, and we can then formulate the equation:
3t + 5(1060-t) = 4500
To solve,
3t + 5300 - 5t = 4500
-2t + 5300 = 4500
-2t = -800
t = 400

Answer 2

There is a way to make a pretty table, and only use one variable, but I am more comfortable using two variables...

So using A - # of adult tickets sold
S - # of student tickets sold

A+S=1060 (number of tickets sold)
$5*A + $3*S = $4500 - revenue generated

If we think a little, we don't have to find both variables, just S, so substituting A = 1060 - S into the 2nd equation;

5(1060 - S) + 3S = 4500
5300 - 5S + 3S = 4500
-2S = 4500 - 5300 = -800
S = (-800)/(-2) = 400.

So there were 400 Student tickets sold.

~i~

Answer 3

Set up two equations. Let a be the number of adult tickets and t be the number of student tickets.

You know that you have 1060 tickets, so you can write the formula as: a + t = 1060.

You also know that a tickets sold at $5 plus t tickets sold at $3 raised a total of $4500, so you can write the formula as 5a + 3t = 4500.

Now you solve the system of equations:
a + t = 1060
5a + 3t = 4500

Solve for one of them (I choose the easier one):
a = 1060 - t

Substitute for the other equation:
5(1060 - t) + 3t = 4500
5300 - 5t + 3t = 4500
2t = 800
t = 400

So you have 400 student tickets.
You can plug that in to figure out the adult tickets (a + 400 = 1050 means that 650 adult tickets were sold).

Answer 4

t represents the number of student tickets sold. Let "a" represent the number of adult tickets sold.

Therefore: a + t = 1060 .... eq1

Since the total amount of tickets sold is 1060 and the money brought in from ticket sales is $4500.00

5*a + 3*t = 4500 ...eq2

From eq1, you get: a = (1060 - t)

Substitute this into eq2, to get:
(1060 - t)*5 + 3*t = 4500
5300 - 5*t + 3*t = 4500
5300 - 2*t = 4500
- 2*t = 4500 - 5300
- 2*t = -800 { / both sides by -2}
t = 400

Answer 5

Let A equal number of adult tickets
Let B equal number of student tickets sold.

Total number of tickets = 1060
Total value of tickets sold = 4500

5A + 3B = 4500
A + B = 1060
A = 1060 - B
Then, step by step, using substitution, and carrying out the math.

5(1060 - B) + 3B = 4500
5300 - 5B + 3B = 4500
5300 -2B = 4500
-2B = -800
B = 400

Answer 6

let x represent the number of adult tickets sold and y represent the student tickets
Since, total of 160 tickers were sold ie x+y=1060;
and also each adult ticket costs $5 and student ticket costs $3 it implies
5x+3y=4500;
=> 5x+3(1060-x)=4500;
=>2x=4500-3180
=>2x=1320;x=660
There fore no of adult tickers sold are 660
Now number of student tickers sold are
1060-660 Since we know x+y=1060
ie.,400

Answer 7

5A + 3S = 4500
A + S = 1060; A = 1060 - S

5 (1060 - S) + 3S = 4500
5300 - 5S + 3S = 4500
5300 - 2S = 4500
5300 - 4500 = 2S
800 = 2S
800/2 = S

S = 400

Answer 8

3t + 5a = 4500
t + a =1060
a= 1060-t
3t+5(1060-t)=4500
3t+5300-5t=4500
2t=800
t=400

Answer 9

let [n] become the senior class ticket sold


5n+3t=4500
n+t=1060

solve for t using either way you like