Question

brad is at the deli, buying lunchmeat and choose for lunch. lunchmeat costs $8 per pound (x), and choose costs $10 per pound (y). he uses the inequality 8x + 10y ≤ 80, to determine the combinations of lunchmeat and choose that he can afford to purchase. which statement is true? the solution (2.75, 6.25) is viable and means that brad can buy 2.75 pounds of lunchmeat and 6.25 pounds of cheese. the solution (2.75, 6.25) is not viable because brad does not have enough to spend $2.75 on lunchmeat and $6.25 on cheese. the solution (6.25, 2.75) is viable and means that brad can buy 6.25 pounds of lunchmeat and 2.75 pounds of cheese. the solution (6.25, 2.75) is not viable because brad does not have enough to spend $6.25 on lunchmeat and $2.75 on cheese.

Explanation:

Step1: Substitute the values into the inequality

For a point \((x,y)\), substitute \(x\) and \(y\) into \(8x + 10y\leq80\).
For the point \((2.75,6.25)\):
\(8\times2.75+10\times6.25\)
\(=22 + 62.5\)
\(=84.5\)
Since \(84.5>80\), this point is not a solution.
For the point \((6.25,2.75)\):
\(8\times6.25+10\times2.75\)
\(=50+27.5\)
\(=77.5\)
Since \(77.5\leq80\), this point is a solution.

Step2: Analyze the meaning of the solution

A solution \((x,y)\) means that when \(x\) is the pounds of lunch - meat (costing \(8\) dollars per pound) and \(y\) is the pounds of cheese (costing \(10\) dollars per pound), the total cost \(8x + 10y\) does not exceed \(80\) dollars. So the solution \((6.25,2.75)\) means Brad can buy \(6.25\) pounds of lunch - meat and \(2.75\) pounds of cheese.

Answer:

The solution \((6.25,2.75)\) is viable and means that Brad can buy \(6.25\) pounds of lunchmeat and \(2.75\) pounds of cheese.