Question

You are considering renting a computer. The first option is to pay a $280 base fee upon

signing the rental agreement plus $15 per week, while the second option is to pay no base fee but to pay
$22 per week. After how many weeks does the first option become the better deal?

Answer 1

Let's start by defining the variables we need for the problem:

$w$: the number of weeks you'll be renting the computer.

$C_1$: the total cost of the first option.

$C_2$: the total cost of the second option.

According to the problem statement, the total cost $C_1$ of the first option is given by a base fee of $280 plus $15 per week:

$$C_1 = 280 + 15w$$

The total cost $C_2$ of the second option is given by a flat fee of $22 per week:

$$C_2 = 22w$$

We want to find out after how many weeks $w$ the first option becomes the better deal. In other words, we want to find the point where $C_1 < C_2$:

$$280 + 15w < 22w$$

Simplifying this inequality, we get:

$$280 < 7w$$

$$w > \frac{280}{7}$$

$$w > 40$$

Therefore, after 40 weeks, the first option becomes the better deal, since the total cost will be lower than the flat rate option.