Question

Adult tickets for a school musical sold $7 and student tickets sold for $4. 150 tickets were sold all together for $891. How many of each type were sold?

Answer 1

Adult ticket were sold = 97 tickets

Student tickets were sold = 53 tickets

Explanation:

Let x be the adult ticket and y be the student ticket.

Adult ticket for $7.

Student ticket for $4.

Total sold ticket = 150

Total sold tickets for $891

Solution:

As per given statement, 150 tickets were sold for $891.

So, total adult ticket and student ticket is equal to 150 tickets:

`x+y=150` ------------(1)

Adult tickets for a school musical sold $7 and student tickets sold for $4.

So, the equation is written as:

`7x+4y=891` ------------(2)

Solve the equation 1 for x.

`x = 150-y` ---------------(3)

Substitute
`x = 150-y` in equation 2.

`7(150-y)+4y=891`

`1050-7y+4y=891`

`1050-3y=891`

Add 3y both side of the equation.

`1050-3y+3y=891+3y`

`1050=891+3y`

`3y=1050-891`

`3y=159`

`y=(159)/(3)`

y = 53 student tickets

Substitute y = 53 in equation 3.

`x=150-53`

x = 97 adult tickets

Therefore, 97 adult tickets and 53 student tickets were sold.

Answer 2

Answer: 81 of each type of ticket was sold

Explanation:

81 × adult tickets ($7) = $ 561

81 × students ticket ($4)= $324