Question

The Frill family and the Smith family go to the movies.

The Frill family buys 6 adult tickets and 2 child tickets for $124.
The Smith family buys 3 adult tickets and 5 child tickets for $100.

Find the prize of an adult ticket and the prize of a child ticket.

Answer 1

Explanation:

Let a be the price of 1 adult ticket.

Let c be the price of 1 child ticket.

given,

`6a + 2c = 124`

as equation 1,

and

`3a + 5c = 100`

as equation 2.

Now we will solve for a and c using elimination method of simultaneous equations.

Now we multiply equation 2 by 2 to eliminate a and solve for c.

`3a * 2 + 5c * 2 = 100 * 2 \\ 6a + 10c = 200`

This new equation will be equation 3.

Now we will use equation 1 - equation 3 to eliminate a and solve for c.

`(6a - 6a) + (2c - 10c) = 124 - 200 \\ 0 + ( - 8c) = - 76 \\ - 8c = - 76 \\ c = - 76 / - 8 \\ = 9.5`

Now substitute c into equation 2.

`3a + 5(9.5) = 100 \\ 3a + 47.5 = 100 \\ 3a = 100 - 47.5 \\ 3a = 52.5 \\ a = 52.5 / 3 \\ = 17.5`

Therefore one adult ticket will cost $17.50 and one child ticket will cost $9.50.