Question

B. At the circus, three adult tickets and five child tickets cost $51, and five adult tickets

and two child tickets cost $47. Which system of linear equations below can be used to
determine the price of each ticket?
Let x represent the cost of an adult ticket, and let y represent the cost of a child ticket.

Answer 1

Answer: x = $7, y = $6

Explanation:

Let x be the cost of an adult ticket

Let y be the cost of a children's ticket

Translate these sentences to algebra:

At the circus, three adult tickets and five child tickets cost $51: 3x + 5y = 51

Five adult tickets and two child tickets cost $47: 5x + 2y = 47

Now we have two equations. Let's use substitution to solve.

3x + 5y = 51

3x = 51 - 5y

.: x = 17 - 5y/3

Now substitute this value of x into the second equation to find the numerical value of y:

5(17 - 5y/3) + 2y = 47

85 - 25y/3 + 2y = 47

-19y/3 = -38

-19y = -114

.: y = 6

Now find x:

x = 17 - 5y/3

x = 17 - 10

.: x = 7

So an adult ticket costs $7, and a child ticket costs $6 :)