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 $2.50x + 3.50y leq 30$ represents the food sales in the first hour. if ben has sold 4 veggie wraps, what is the maximum number of turkey sandwiches ben could have sold? 10 6 7 5

Explanation:

Step1: Substitute y = 4 into the inequality

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

Step2: Simplify the left - hand side

First, calculate \(3.50\times4=14\). So the inequality becomes:
\(2.50x + 14 \leq 30\)

Step3: Isolate the term with x

Subtract 14 from both sides of the inequality:
\(2.50x\leq30 - 14\)
\(2.50x\leq16\)

Step4: Solve for x

Divide both sides of the inequality by 2.50:
\(x\leq\frac{16}{2.50}\)
\(\frac{16}{2.50}=\frac{160}{25}=\frac{32}{5} = 6.4\)
Since x represents the number of turkey sandwiches, it must be a non - negative integer. So the maximum value of x is 6.

Answer:

6