Question

braden bought three adult tickets and one child ticket at the movie theater and paid $32. karen bought seven adult tickets and two child tickets and paid $73. find the cost for one child ticket

Answer 1

Answer: $5

Explanation:

Let the cost of one adult ticket be x and the cost of one child ticket be y , then from the first statement:

`3x + y = 32`

And from the second statement , we have

`7x + 2y = 73`

combining the two equations , we have

`3x + y = 32` ........................... equation 1

`7x + 2y = 73` ........................... equation 2

Solving the system of linear equation by substitution method , from equation 1 , make y the subject of the formula ,that is

`y = 32 - 3x` ............................... equation 3

substitute equation 3 into equation 2 , equation 2 then becomes

`7x + 2 ( 32 - 3x )` =
`73`

`7x + 64 - 6x = 73`

`x + 64 = 73`
`x = 73 - 64`

`x = 9`

Substitute
`x = 9` into equation 3 to find the value of y

`y = 32 - 3x`

`y = 32 - 3(9)`

`y = 32 - 27`

`y = 5`

Therefore : the cost of one child ticket is $5