Question

DVD Rentals You belong to an online DVD rental service. Your yearly rental budget is \(200. Each rental costs \)4.

a. Copy and complete the table.

b. Write a variable expression for the cost of r rentals.

c. Write a variable expression for the amount of your budget left after r rentals.

d. Writing How many DVDs will you be able to rent before the $200 is spent? Explain how you found your answer.

Short answer

(a) The complete table is obtained as:

(b) The variable expression for cost of r rentals is $C=4·r$

(c) The variable expression is $A=200-4·r$

(d) The number of DVD which can be rented before the $200 is spent is 50.

Step-by-step solution

(a)Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given

The total yearly rental budget is $200 and each rental cost is $4.

Step-3 – Complete the table

From, the table, it can be observed that in Cost (dollars) column, total rental cost is written which is a product of number of DVDs and rental cost of each DVD and Amount left (dollars) column is obtained by subtracting the cost of DVDs from $200.

Hence, the complete table is obtained as:

(b)Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given

The total yearly rental budget is $200 and each rental cost is $4.

Step-3 – Find expression

From, the table, it can be observed that in Cost (dollars) column, total rental cost C is written which is a product of number of DVDs, r and rental cost of each DVD that is $4.

Hence, the variable expression for cost of r rentals is obtained as $C=4·r$.

(c)Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given

The total yearly rental budget is $200 and each rental cost is $4.

Step-3 – Find expression

From, the table, it can be observed that in Cost (dollars) column, Amount left (dollars) column is obtained by subtracting the total cost of DVDs, C from $200.

Total cost is obtained as:

$C=4·r$

Hence, the variable expression is obtained as:

$\begin{array}{l}A=200-C\\ A=200-4\cdot r\end{array}$

(d)Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given

The total yearly rental budget is $200 and each rental cost is $4.

Step-3 – Find number of DVD

Therefore, the variable expression for cost of r rentals is obtained as:

$C=4·r$

Since, $C=200$ as $200 is spent. Then r gives the total number of DVDs which can be rented before $200 is spent.

So,

$\begin{array}{l}r=\frac{200}{4}\\ r=50\end{array}$

Hence, the number of DVD which can be rented before the $200 is spent is 50.