Question

Alice can rent a golf bag for $14 plus $28 for each hour of use (prorated as

applicable). Alice will rent the golf bag for at least one hour.
Suppose C (x) models the amount Alice spends renting the golf bag where
is the number of hours of use. If Alice has $112.00 to spend, what is the
domain of C (x)? Use inequality notation.

Answer 1

To find the domain of C(x) in this scenario, we need to consider the amount of money Alice has to spend and the rental cost associated with the number of hours of use.

Let's break it down:

Alice can rent the golf bag for $14 plus $28 for each hour of use. Since she has $112.00 to spend, we can set up an equation:

C(x) = 14 + 28x, where x is the number of hours of use.

To determine the domain of C(x), we need to find the range of x values that makes C(x) less than or equal to $112.00. In other words, we need to find the values of x that satisfy:

C(x) ≤ 112

Substituting the expression for C(x), we have:

14 + 28x ≤ 112

Simplifying the inequality:

28x ≤ 98

Dividing both sides by 28:

x ≤ 98/28

Simplifying further:

x ≤ 7/2

The domain of C(x) is x ≤ 7/2, or in interval notation, x ∈ (-∞, 7/2]. This means Alice can rent the golf bag for any number of hours up to and including 7/2 (or 3.5) hours.

CROWN ME!!