Question

eli and his children went into a restaurant where they sell drinks for $2 each and tacos for $3.50 each. eli has $45 to spend and must buy no less than 15 drinks and tacos altogether. write a system of linear inequalities to represent the situation. answer attempt 1 out of 2 2x + 3.50y \boxed{} \boxed{} x + y \boxed{} \boxed{}

Explanation:

Step1: Define variables

Let \( x \) be the number of drinks and \( y \) be the number of tacos.

Step2: Cost constraint

The cost of drinks is \( \$2 \) each and tacos is \( \$3.50 \) each, and Eli has \( \$45 \) to spend. So the cost inequality is \( 2x + 3.50y \leq 45 \).

Step3: Quantity constraint

They must buy no less than 15 drinks and tacos altogether, so \( x + y \geq 15 \).

Step4: Non - negativity constraints

Since the number of drinks and tacos can't be negative, \( x \geq 0 \) and \( y \geq 0 \). But usually, for this problem, the main constraints are the cost and the quantity constraints.

Answer:

The system of linear inequalities is:
\(

$$\begin{cases}2x + 3.5y\leq45\\x + y\geq15\\x\geq0\\y\geq0\end{cases}$$

\) (If we consider non - negativity, but the key ones are \( 2x + 3.5y\leq45 \) and \( x + y\geq15 \))