4. Tickets at a particular movie theater have different rates for adults are children. On Thursday, the theater sold 2 adult tickets and 6 child ticket for $56. The next day, the theater sold 3 adult tickets and 7 children tickets for $72. What is the price for the adult ticket and the price for

the child ticket?

adult ticket price: $10

child ticket price: $6

Step-by-step explanation:

let's say an adult ticket costs a dollars and a child ticket costs c dollars

cost of 2 adult tickets = a dollars for each ticket = a + a = 2a

cost of 6 child tickets = 6c

thursday's sales:

2a + 6c = 56

friday's sales (the next day):

3a + 7c = 72

we now have a system of equations

2a + 6c = 56

3a + 7c = 72

divide both sides by 2 in the first equation to simplify it

a + 3c = 28

subtract 3c from both sides to solve for a

a = 28 - 3c

plug that into the second equation to remove a variable

3(28-3c) + 7c = 72

84 - 9c + 7c = 72

84 - 2c = 72

subtract 84 from both sides to isolate the variable and its coefficient

-2c = -12

divide both sides by -2 to solve for c

c = 6

a = 28 - 3c

  = 28 - 3 * 6

   = 10

step-by-step explanation: