Question

At a local fair, the admission fees are $1.50 for children, $3 for college students, and $5 for adults. On Saturday, 1500 tickets were sold and brought in $5500. The number of college student tickets sold was 100 less than the number of children's tickets sold.

Answer 1

Answer:

Number of children tickets = 400

Number of students tickets = 300

Number of adults tickets = 800

Step-by-step explanation:

Let the number of children tickets = $x$

Let the number of students tickets = $y$

Let the number of adults tickets = $z$

Total number of tickets sold = 1500

Writing the equation:

$x+y+z=1500$ .... (1)

Price for each children ticket = $1.50

Price for each student ticket = $3

Price for each adult ticket = $5

Total money brought in = $5500

$1.5x+3y+5z = 5500$ ..... (2)

Number of student tickets sold was 100 lesser than number of children's tickets.

i.e.

$y = x -100$ ..... (3)

Putting value of $y$ from (3) in equation (1) and equation (2):

$x+x-100+z=1500\\\Rightarrow 2x+z=1600 .... (4)$

$1.5x+3(x-100)+5z=5500\\\Rightarrow 4.5x+5z=5800 ..... (5)$

Multiplying equation (4) by 5 and subtracting equation (5) from it:

$5.5x=2200\\\Rightarrow x = 400$

By equation (3):

$y = 400 - 100 = 300$

By equation (1):

$z = 1500 - 400 - 300 = 800$

Therefore, the answer is:

Number of children tickets = 400

Number of students tickets = 300

Number of adults tickets = 800