Question

1000 tickets were sold. Adult tickets cost $8.50, children's tickets cost $4.50, and a total of $7300 was collected. How many tickets of each kind were sold?

Answer 1

Adult`=700`
Children`=300`

Explanation:

`a =`Adult
`c=`Children

Then-

`a+c=1000` ---------------------------(1)
`8.50a+4.50c = 7300`-----------(2)

Solve the equation (1) for c
`c = 1000-a`
Substitute the value of c in equation (2)
`8.50a+4.50(1000-a) = 7300`
`8.50a+4500-4.50a) = 7300`
`4a = 7300-4500 = 2800`
`a=2800/4=700`

Substitute the value of a in equation (1)

`700+c=1000`
`c=1000-700=300`

Answer 2

`700` adult tickets and
`300` children's tickets

Explanation:

Define:
`color(white)("XXX")a = "number of adult tickets"`
`color(white)("XXX")c = "number of children's tickets"`

We are told:
[1]`color(white)("XXX")a+c=1000`
and
[2]`color(white)("XXX")850a+450c=730000`

Simplifying [2] by dividing by `50`
[3]`color(white)("XXX")17a+9c=14600`

Multiply [1] by 9
[4]`color(white)("XXX")9a+9c=9000`

Subtract [4] from [3]
[5]`color(white)("XXX")8a = 5600`

Divide by `8`
[6]`color(white)("XXX")a = 700`

Substitute `700` for `a` in [1] and simplify
[7]`color(white)("XXX")c=300`