Question

Solve using a system of equations. Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. If 110 tickets were sold for a total of $615.00, how many tickets of each type were sold

Answer 1

The number of adults tickets is 80 and the number of students tickets is 30

Explanation:

Given as :

The tickets price for adults = $6.00

The tickets price for students = $4.50

Total number tickets were sold = 110

Total Price of 110 tickets = $615.00

Now,

Let The number of adults tickets sold = A

The number of students tickets sold = S

So, according to question

A + S = 110

And 6 A + 4.5 S = 615

Or, 6 A + 6 S = 660 .....1

6 A + 4.5 S = 615 ......2

Solving the equations

( 6 A + 6 S ) - ( 6 A + 4.5 S ) = 660 - 615

Or, ( 6 A - 6 A ) ( 6 S - 4.5 S ) = 45

or, ( 6 S - 4.5 S ) = 45

or, 1.5 S = 45

∴ S =
`(45)/(1.5)`

I,e S = 30

Put the value of S in eq 1

So, 6 A + 6 × 30 = 660

Or, 6 A = 660 - 180

Or 6 A = 480

∴ A =
`(480)/(6)`

I.e A = 80

Hence The number of adults tickets is 80 and the number of students tickets is 30 . Answer