Chapter 2.4, Problem 6STP

Admission for a water park is $17.50 per day. A season pass costs $125. A locker rental costs $3.50 per day.

a. What is an equation that represents the relationship between the cost of a daily pass and the cost of a season pass?

b. How many days would you have to go to the water park for the season pass to save you money?

To determine

To calculate:Admission for a water park is $17.50 per day. A season pass costs $125. A locker rental costs $3.50 per day. What is an equation that represents the relationship between the cost of a daily pass and the cost of a season pass?

Answer to Problem 6STP

  $17.50t=125$

Explanation of Solution

Given information: Let $t$ be the number of days you go to the water park.

Calculation: Total cost of a daily pass = admission charge + locker rent, i.e.

Total cost of a daily pass $=17.50+3.50$

  $=21$

So, total cost of daily passes for $t$ days $=21t\mathrm{...}(i)$

Total cost of season pass = cost of season pass + per day locker rent, i.e.

Total cost of season pass for $t$ days $=125+3.50x\mathrm{...}(ii)$

Equating both equations, we get

  $21t=125+3.50x$

  $17.50t=\mathrm{125...}(iii)$

To determine

To calculate:Admission for a water park is $17.50 per day. A season pass costs $125. A locker rental costs $3.50 per day. How many days would you have to go to the water park for the season pass to save you money?

Answer to Problem 6STP

a person has to go at least 8 days to save money.

Explanation of Solution

Given information: From above part we know that the relationship between the cost of a daily pass and the cost of a season pass is $17.50t=125$

Now we solve the above equation

  $17.50t=125$

  $t=7.14$

So a person has to go more than 7.14 days , so a person has to go at least 8 days to save money.