Question

Amusement Parks You are trying to decide whether to pay $120foraseasonpasstoanamusementpark.Ifyoubuythepass,yougetanunlimitednumberofvisitstotheparkandreducedparkingfor$8. If you do not buy the pass, you pay $23admissionand$10 for parking each time you visit the park. After how many visits to the park will the cost of visiting with the season pass be less than cost of visiting without the season pass?

1. Write a variable expression for the cost of making v visits to the park if you don’t buy a season pass.
2. Write an inequality in terms of v showing that the cost of visiting the park with a season pass is less than the cost of visiting the park without a season pass.
3. Solve the inequality.

Short answer

1. The variable expression for cost of making v visits to the park if you don’t buy a season pass is:$23v+10v=33v$ .
2. The required inequality is$120+8v<23v+10v$:
3. The solution is$v>4.8$

Step-by-step solution

Step-1 – Given

Given that:

The cost of season pass is$120$

The parking rate with season pass is $8$

The rate without season pass per visit is $23$

The parking rate without season pass is $10$.

Step-2 – To determine

We have to create an equation for the case if we don’t buy the season pass.

Step-3 – Calculation

Let v = the number of visits to the park if we don’t buy a season pass.

So the required expression for the cost of making visits to the park without buy a season pass is given by $23v+10v=33v$

Step-1 – Given

Given that:

The cost of season pass is $120$

The parking rate with season pass is $8$

The rate without season pass per visit is 23.

The parking rate without season pass is 10 .

Step-2 – To determine

We have to create an inequality for the case if we buy the pass.

Step-3 – Calculation

Let v = the number of visits to the park if we buy a season pass.

So, $120+8v<23v+10v$

Step-1 – Given

Given that:

The cost of season pass is 120

The parking rate with season pass is 8

The rate without season pass per visit is 23

The parking rate without season pass is 10 .

Step-2 – To determine

We have to solve the inequality in b.

Step-3 – Calculation

$\begin{array}{l}120+8v<33v\\ 120+8v-8v<33v-8v\\ 120<25v\\ v>\frac{120}{25}\end{array}$

$v>4.8$