If the total receipts for the day were $891.25, how many of each kind of ticket were sold?

Question

The owner of a movie theater was counting the money from one day's ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost $7.50 each and children's tickets cost $4.75 each.

Answer 1

Hello Jay,

 

let x represent number of the adults tickets sold

let y represent the children tickets sold

 

x+y=150

 

now based on price of tickets

 

$7.5(x)+$4.75(y)=$891.25

 

you now have two equations

 

7.5x+4.75y=891.25

    x   +    y=150

 

to work this multiple the second equation (x+y=150) by the negative value of either x or y in the first equation...I will use the value of x so it will be multiplied by (-7.5)

  7.5x+4.75y=891.25

-7.5(x+y=150)

 

  7.5x+4.75y=891.25

-7.5x+-7.5y=-1125

===============  add the equations

          -2.75y=-233.75.....to find y divide both sides by -2.75

y=85

y=children's tickets=85 children's tickets sold

 

substitute to find value of x

 

x+85=150

  -85=-85

======= add again

x=65

 

x= adult tickets sold=65 tickets

 

to check

$7.50(65)+$4.75(85)=$891.25

$487.50+$403.75=$891.25...check

 

hope you understood and it helped

Answer 2

State your initial equations:

Total of adult and child tickets sold is 150

A + C=150

The total of the ticket sales is $891.25

7.5A + 4.75C = 891.25

 

Restate one of the formulas (You can pick either one. I chose A:)

A = 150-C

 

Substitute:

7.5 (150-C) + 4.75C = 891.25

 

Distribute:

1125 - 7.5C + 4.75C = 891.25

 

Combine Like Terms:

1125 - 2.75C = 891.25

 

Isolate the variable:

-2.75C = 891.25-1125

 

Combine Like Terms (again):

-2.75C = -233.75

 

Divide to find "C":

C = -233.75/-2.75

C = 85

 

Now use the value for "C" to find "A":

A=150-C

A=150-85

A=65

 

Now test if A=65 and C=85 are correct"

7.5A + 4.75C = 891.25

7.5(65) + 4.75(85) = 891.25

487.5 + 403.75 = 891.25

891.25 = 891.25

 

So the correct answer is 65 Adult tickets and 85 Child tickets.