Question

turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. let x represent the number of turkey sandwiches and y represent the number of veggie wraps. the inequality 2.50x + 3.50y ≤ 30. if ben has sold 4 veggie wraps, what is the maximum number of turkey sandwiches ben could have sold? 5, 6, 7, 10

Explanation:

Step1: Substitute y = 4 into the inequality

We know the inequality is \(2.50x + 3.50y \leq 30\) and \(y = 4\). Substitute \(y = 4\) into the inequality:
\(2.50x + 3.50\times4 \leq 30\)

Step2: Simplify the left - hand side

First, calculate \(3.50\times4=14\). Then the inequality becomes \(2.50x+14\leq30\).
Subtract 14 from both sides of the inequality: \(2.50x\leq30 - 14\), so \(2.50x\leq16\).

Step3: Solve for x

Divide both sides of the inequality \(2.50x\leq16\) by 2.50: \(x\leq\frac{16}{2.50}\).
\(\frac{16}{2.50}=\frac{16\times2}{2.50\times2}=\frac{32}{5} = 6.4\)
Since \(x\) represents the number of turkey sandwiches, \(x\) must be a non - negative integer. So the maximum value of \(x\) is 6.

Answer:

6 (corresponding to the option "6")