A student was working on the problem below: Mr. Braun has $85.00 to spend on pizzas and soda pop for a picnic. Pizzas cost $11.00 each and the drinks cost $0.90 each. Four times as many drinks as pizzas are needed. What is the maximum number of pizzas that Mr. Braun can buy? The student began by writing the let statement: Let x = # of pizzas Then the student wrote the inequality: \displaystyle 11.00(x)+0.90(4x)\ge85.0011.00(x)+0 .90(4x)≥85.00 The student made a MISTAKE. Describe the student's error and explain how you know it's wrong. (Do not solve the inequality.)

11x + 0.90(4x) ≤ $85

Step-by-step explanation:

Let the number of pizzas be represented by p

Let the number of sodas be represented by s

Mr. Braun has $85.00 to spend on pizzas and soda pop for a picnic. Pizzas cost $11.00 each and the drinks cost $0.90 each.

$11 × p + $0.90 × s = $85

11x + 0.90y ≤ $85Equation 1

Four times as many drinks as pizzas are needed.

4p = s

We substitute 4p for s in Equation 1

11x + 0.90(4p) ≤ $85

What is the maximum number of pizzas that Mr. Braun can buy?

The maximum number of pizzas Mr Braun can buy =

11x + 0.90(4p) ≤ $85

The student's error has to do with the inequality sign. The student used greater than or equal to.

The correct sign is less than or equal to because Mr Braun has only $85 to spend.