Question

The regular price of a child's entry ticket to a water park is $9 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 $132 for 1 adult ticket and 4 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:

132 = one-halfx + 2(x − 9)

What is the regular price of a child's ticket?
$60 $57 $51 $42

Answer 1

Regular Price of a child's ticket is: x-9
Regular Price for adult ticket is : x

Using the give equation, you should solve for the value of \(\sf \color{red}{x}\) first:

\(\sf 132 = \frac{1}{2}x + 2(x − 9)\)

Distribute the coeffficient into the terms inside the bracket:

\(\sf 132 = \frac{1}{2}x + 2x − 18\)

Collect like terms:

\(\sf 132 +18 = \frac{1}{2}x + 2x\)

Simplify:

\(\sf 150= \frac{5}{2}x\)

Solve for x:
\(\sf 300=5x\\x=60\)


Solve for the regular price of the child's ticket:

\(\sf \color{red}{Child's\ ticket=x-9}\) (just plug in x=60, and solve)