whats the answer

Question

An amusement park offers a yearly membership of $275 that allows for free parking and admission to the park. Members can also use the water park for an additional $5 per day. Nonmembers pay $6 for parking, $15 for admission, and $9 for the water park.

a) Write and solve an equation to find the number of visits 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.

Answer 1

This problem involves setting up the equation and solving for a variable. The variable in this case is number of days. Let's first set up the equation for how much a yearly membership costs. We will assign the total cost of a yearly membership to y1 and the total number of days attended to x.

y1 = 275 + 5x

The 275 is from the yearly membership charge, a static charge. The 5x term represents the cost of going to the water park for x days. For example, if they went to the water park twice, then this cost would be 5*2 = $10 dollars.

Now let's set up the equation for non-members. Non-members have to pay $6 for parking, $15 for admission, and $9 for the water park. We will assign the total cost of a non-member to y2 and the total number of days attended to x.

y2 = 6x + 15x + 9x

y2 = 30x

Here, it is known that on each visit, the person must park (6x), pay admission (15x), and pay for the water park (9x). These costs can be added up as 30x.

To find when the total cost is the same for a member or non-member, set y1 equal to y2.

y1 = y2

275 + 5x = 30x

Subtract 5x from both sides of the equation

275 = 25x

Divide both sides by 25.

x = 11 days

Answer 2

5x + 275 = 30x