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

Answer:

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

Step-by-step 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 = $\frac{45}{1.5}$

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 = $\frac{480}{6}$

I.e A = 80

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