Question

Under her cell phone plan Nelly pays a flat cost of $41.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month. Write and solve inequality which can be used to determine g. The number of gigabytes Nelly can use while staying within her budget

Answer 1

To determine the maximum number of gigabytes \( g \) that Nelly can use while keeping her monthly bill under $50, we can set up the inequality based on her cell phone plan costs.

Nelly's total monthly bill consists of a flat cost and a variable cost based on the number of gigabytes used. The equation for her total monthly bill can be expressed as:

\[
\text{Total Bill} = \text{Flat Cost} + (\text{Cost per GB} \times g)
\]

Substituting the values into the equation:

\[
\text{Total Bill} = 41.50 + 5g
\]

We want to keep the total bill under $50, so we write the inequality:

\[
41.50 + 5g < 50
\]

Now, let's solve for \( g \):

1. Subtract 41.50 from both sides:
\[
5g < 50 - 41.50
\]
\[
5g < 8.50
\]

2. Now, divide both sides by 5:
\[
g < \frac{8.50}{5}
\]
\[
g < 1.70
\]

Since \( g \) must be a non-negative whole number (as it represents gigabytes), the maximum integer value for \( g \) that satisfies the inequality is:

\[
g \leq 1
\]

Thus, Nelly can use a maximum of **1 gigabyte** while staying under her budget of $50.