Question

13.) Springfield Elementary is putting on a school play

to raise money for their field trip. They are selling
adult's tickets for $6 and children's tickets for $3.50.
They made a total of $550 for selling 125 tickets. Write
and solve a system to determine how many of each
type they sold.

Answer 1

45 adult tickets and 80 children tickets were sold

Solution:

Let "a" be the number of adult tickets sold

Let "c" be the number of children tickets sold

Cost of 1 adult ticket = $ 6

Cost of 1 children ticket = $ 3.50

They sold a total of 125 tickets

Therefore,

a + c = 125

c = 125 - a --------- eqn 1

They made a total of $550. Therefore, frame a equation as:

number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = 550

`a * 6 + c * 3.50 = 550\\`

6a + 3.50c = 550 ----------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

6a + 3.50(125 - a) = 550

6a + 437.5 - 3.50a = 550

2.5a = 112.5

a = 45

Substitute a = 45 in eqn 1

c = 125 - 45

c = 80

Thus 45 adult tickets and 80 children tickets were sold