$\"\"$

An amusement park offers a yearly membership of $\"\"$ that allows for free parking and admission to the park.

Members can also use the water park for an additional $\"\"$ per day.

Nonmembers pay $\"\"$ for parking, $\"\"$ for admission, and $\"\"$ for the water park.

It would take for the total cost to be the same for a member and a nonmember if they both use the water park at each visit.

Write an equation.

Let $\"\"$ is the number of visits.

The cost for $\"\"$ visits for a member is represented by the expression $\"\"$ .

The cost for $\"\"$ visits for a nonmember is represented by the expression $\"\"$ .

The cost is same for a member and a non-member.

The equation is $\"\"$ .

$\"\"$

Find the number of visits.

$\"\"$ (Orginal equation)

$\"\"$ (Add inside terms)

$\"\"$ (Subtract $\"\"$ from each side)

$\"\"$ (Apply additive inverse property : $\"\"$ )

$\"\"$ (Divide each side by $\"\"$ )

$\"\"$ (Simplify)

The total cost would be the same for a member and a nonmember if they both use the water park at each visit for $\"\"$ visits.

$\"\"$

Make a table for the costs of members and nonmembers after $\"\"$ and $\"\"$ visits to the park.

Tabular form:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Visits	Cost for members	Cost for nonmebers
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$

Observe the table:

The ordered pairs of cost for members are $\"\"$ .

The ordered pairs of cost for nonmembers are $\"\"$ .

$\"\"$

Graph:

Plot these points on a coordinate graph.

Graph the number of visits on the $\"\"$ -axis and the cost on the $\"\"$ -axis.

Graph:

$\"\"$

Note:

The dots in pink color denote cost of the member in the amusement park.

The dots in blue color denote cost of the non-member in the amusement park.

Observe the graph:

The ordered pairs of cost for members are $\"\"$ .

The ordered pairs of cost for nonmembers are $\"\"$ .

Both functions are linear.

The points for non-members are lower than the points for members when $\"\"$ is less than $\"\"$ .

Therefore, if a person is going to visit the park less than $\"\"$ times, it will be cheaper to be a nonmember.

If a person is going to visit the park more than $\"\"$ times, it will be cheaper to be a member.

$\"\"$

a.The total cost would be the same for a member and a nonmember if they both use the water park at each visit for $\"\"$ visits.

b.Tabular form:

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Visits	Cost for members	Cost for nonmebers
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$

c.Graph:

$\"\"$

If a person is going to visit the park less than $\"\"$ times, it will be cheaper to be a nonmember.

If a person is going to visit the park more than $\"\"$ times, it will be cheaper to be a member.