Question

Movie tickets for 2 adults and 3 children cost $44.50. Tickets for the same movie cost $25.50 for 1 adult and 2 children. (a) Let a represent the cost of a ticket for an adult and c represent the cost of a ticket for a child. Write a system of equations that can be used to find a and c. (b) What is the total cost of tickets for 1 adult ticket and 1 child ticket?

Answer 1

Answer:

a) 2a + 3c = $44.50

     a + 2c + $25.50

b) $19

Step-by-step explanation:

Simultaneous equations. A = adult. C = children

2a + 3c = $44.50 (EQUATION 1)

a + 2c = $25.50 (EQUATION 2)

Now solve this using the method of elimination:

2a + 3c = $44.50 (EQUATION 1)

a + 2c = $25.50 (EQUATION 2)

Multiply equation 2 by 2 so that both equations have the same a coefficient.

2a + 4c = $51 (NEW EQUATION 2)

Now subtract equation 1 from equation 2:

2a - 2a + 4c - 3c = $51 - $44.50 (2a cancels out)

c = $6.50

Now substitute c into one of the equation, in this case, I'm using original equation 2.

a + 2($6.50) = $25.50

a + $13 = $25.50

a = $12.50

Total cost of one adult and child = $6.50 + $12.50

                                                       = $19