Which inequality represents all possible combinations of x, the number of sausage links that will be cooked on the grill, and y, the number of briskets that will also be cooked?

Understand the Problem

The question is asking which inequality accurately represents the weight constraint of sausage links and briskets being cooked on a grill, where x is the number of sausage links (2 lb each) and y is the number of briskets (6 lb each). We need to formulate an inequality that accounts for the total weight not exceeding 120 lb.

Answer

The inequality representing the weight constraint is: $$ 2x + 6y \leq 120 $$

Steps to Solve

Identify the weight of each item
Sausage links weigh 2 lb each (denote as $2x$) and briskets weigh 6 lb each (denote as $6y$).
Set up the equation for total weight
The total weight of the sausage links and briskets combined must not exceed 120 lb. The equation representing this is:
$$ 2x + 6y \leq 120 $$
Rearranging the inequality
To further simplify, you can divide the entire inequality by 2:
$$ x + 3y \leq 60 $$
However, sticking to the original form is also acceptable for this question.
Identify inequalities from the choices
Based on the setup, look at the available choices:

$6x + 2y \leq 120$
$2x + 6y \leq 120$
$6x + 2y \geq 120$
$2x + 6y \geq 120$
Only the second option matches our established inequality ((2x + 6y \leq 120)).

The correct inequality is:
$$ 2x + 6y \leq 120 $$

More Information

This inequality shows that, for every combination of sausage links ($x$) and briskets ($y$) cooked on the grill, their combined weight must not exceed 120 pounds. This setup is important for managing cooking limits in the restaurant.

Tips

Misunderstanding the weight of each item: Double-check the weights assigned to $x$ and $y$.
Confusing inequality symbols: It’s essential to remember that the total weight must be less than or equal to 120, not greater than.

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