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