Question

The Glee Club budgeted \(\$ 250\) for food for the annual Spaghetti Supper. Each meal costs \(\$ 1.75\) to prepare. Which inequality represents the number of meals that can be prepared without going over the budget? (A) \(x \leq 143\) (B) \(x \geq 143\) (C) \(x \leq 142\) (D) \(x \geq 142\)

Short answer

The correct inequality to represent the number of meals that can be prepared without going over the budget is \(x \leq 142\). Therefore, answer choice (C) is correct.

Step-by-step solution

Mathematical Representation

Let x represent the number of meals. The total cost of preparing the meals is given by \(1.75x\). This total cost must be less than or equal to the total budget of $250. This can be represented by the inequality \(1.75x \leq 250\).

Solving the Inequality

Now, to solve for x, the inequality \(1.75x \leq 250\) can be rewritten by dividing each side by 1.75, resulting in \(x \leq 250/1.75\). Using the rules of arithmetic, divide 250 by 1.75 to get \(x \leq 142.85\).

Interpretation

Since x represents the number of meals, and it is not practical to have a fraction of a meal, x must be a whole number. Hence, the number of meals must be equal to or less than 142. Thus, the inequality representing the number of meals that can be prepared without going over the budget is \(x \leq 142\)