Question

The Singh family and the Peterson family go to the cinema. The Singh family buy 2 adult tickets

and 3 child tickets. They pay £28.20 for the tickets. The Peterson family buy 3 adult tickets and 5
child tickets. They pay £44.75 for the tickets.
Find the cost of each adult ticket and each child ticket.

Answer 1

Adult Tickets Cost £6.75 each

Child Tickets Cost £4.90 each

Explanation:

Let

price of adult tickets be "a"

price of child tickets be "c"

2 adult and 3 child equals 28.2, so we can write:

2a + 3c = 28.20 [equation 1]

also,

3 adult and 5 child equals 44.75, so we can write:

3a + 5c = 44.75 [equation 2]

We multiply first equation by -3 to get:

-3 [2a + 3c = 28.20] = -6a - 9c = -84.6

Then we multiply second equation by 2, to get:

2 [3a + 5c = 44.75] = 6a + 10c = 89.50

Now we add up the 2 new equations:

-6a - 9c = -84.6

6a + 10c = 89.50

-------------------------

c = 89.50 - 84.60 = 4.9

Now, we plug in c = 4.9 into first equation and solve for a:

2a + 3c = 28.20

2a + 3(4.9) = 28.20

2a + 14.7 = 28.20

2a = 13.5

a = 6.75

So,

Adult Tickets Cost £6.75 each

Child Tickets Cost £4.90 each