Question

The regular price of a child's entry ticket to a water park is $6 less than that for an adult's. The park offers half off all entry tickets during the off-peak season. The Sandlers paid a total of $78 for 1 adult ticket and 2 child's tickets to the water park during the off-peak season. The following equation represents this situation, where x represents the regular price of an adult ticket: 78 = one-half x + (x − 6)

Answer 1

let the price of adult's ticket be
`x`
the expression for the child's ticket is
`x-6`

The price of adult's ticket during off-peak season is
`(1)/(2)x`
The price of child's ticket during off-peak season is
`(1)/(2)(x-6)`

The total cost paid by The Sandlers is $78
The equation is
`78= (1)/(2)x- (1)/(2)(2(x-6))` =
`(1)/(2)x+(x-6)`

rearranging to solve the equation

`78= (1)/(2)x+x-6`

`78= (3x)/(2) -6`

`78+6= (3x)/(2)`

`(84)(2)=3x`

`(168)/(3) =x`

`x=56`

The price of one adult's ticket is $56 (normal price) and the price of one child's ticket is $50