Word problem help algebra

Question

At the movie theatre, child admission is $5.10 and adult admission is $8.50 . On Friday, 172 tickets were sold for a total sales of $1128.80 . How many adult tickets were sold that day?

Answer 1

You will need a system of equations.

 

172 tickets, x child, y adult

$1128.80 sales, $5.10x (dollars per child), $8.50y (dollars per adult)

 

1128.80=5.10x+8.50y

172=x+y

 

 

Multiply the top equation by 10 and the bottom by 51

 

11288=51x+85y

8772=51x+51y

 

Subtract the bottom equation from the top

 

2516=34y

74=y

 

Plug it into either equation and solve for x

 

172=x+74

98=x

 

Plug both into the other equation, and check your answer

 

1128.80=5.10(98)+8.50(74)

1128.80=499.80+629

1128.80=1128.80

11288=51x+85y

Answer 2

Another way to think of this is..

 

If all of the tickets were sold at the lower price, the total would be 172 x $5.10 = $877.20. Clearly this is not enough money; in fact, we are short by $1128.80 - $877.20 = $251.60. This total difference has to be made up by the difference in the price of tickets, $8.50 - $5.10 = $3.40. 

 

This means that 74 adult tickets ( = $251.60 / $3.40 ) had to be sold to make up the difference.

Answer 3

Let a = {number of child tickets} and b = {number of adult tickets}

The equation for total revenue is pq where p is the price and q is the quantity.

We are given, 1128.80 = p172 where q = 172

 

p = 1128.80/172 = 6.563

 

6.563(a+b) = 1128.80

 

6.563a + 6.563b = 1128.80

5.1a + 8.5b = 1128.80

 

We can now find the number of adult tickets

 

6.563a + 6.563b = 1128.80

(-1.287)5.1a + 8.5b = 1128.80

 

6.563a + 6.563b = 1128.80

-6.563a - 10.939b = -1452.76

-4.376b = -323.96

b = 74.031

 

Therefore, about 74 adult tickets were sold. I recommend using MATLAB or Octave to get a more precise answer.