Question

nala can spend no more than $150 per month on gasoline. she has already purchased $60 in gas this month. which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30?

• \\(60n + 30 \ge 150\\)
• \\(30n + 60 \ge 150\\)
• \\(30n + 60 \le 150\\)
• \\(60n + 30 \le 150\\)

Explanation:

Identify the variable and rate

Using the Writing Linear Inequalities knowledge point
Let \(n\) represent the number of additional fill-ups Nala purchases. Since each fill-up costs \(\$30\), the variable cost is:

$$ 30n $$

Account for the initial amount

Using the Writing Linear Inequalities knowledge point
Nala has already spent \(\$60\) on gasoline. Adding this fixed cost to the variable cost gives the total amount spent:

$$ 30n + 60 $$

Apply the budget constraint

Using the Real-world Inequality Constraints knowledge point
The phrase "no more than" means the total spending must be less than or equal to \(\$150\):

$$ 30n + 60 \le 150 $$

Answer:

• (A) \(60n + 30 \ge 150\)
• (B) \(30n + 60 \ge 150\)
• (C) \(30n + 60 \le 150\) (Correct answer)
• (D) \(60n + 30 \le 150\)