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 $\frac{1}{2}x$
The price of child's ticket during off-peak season is $\frac{1}{2}(x-6)$

The total cost paid by The Sandlers is $78
The equation is $78= \frac{1}{2}x- \frac{1}{2}(2(x-6))$ = $\frac{1}{2}x+(x-6)$

rearranging to solve the equation
$78= \frac{1}{2}x+x-6$
$78= \frac{3x}{2} -6$
$78+6= \frac{3x}{2}$
$(84)(2)=3x$
$\frac{168}{3} =x$
$x=56$

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