Question

Angie and her sister have \(15 to spend on pizza. A medium pizza costs \)11.50 plus $0.75 per topping. What is the maximum number of toppings Angie and her sister can get on her pizza?

Short answer

Angie and her sister can get a maximum of 4 toppings.

Step-by-step solution

Step 1. State the concept of linear inequalities.

Alinear inequalityis a mathematical statement that relates a linear expression as either less than or greater than another.

A solution to a linear inequality is a real number that will produce a true statement when substituted for the variable. Linear inequalities have either infinitely many solutions or no solution.

Step 2. Form the inequality from the given information. 

Assume the maximum number of toppings to be ‘x’.

A medium pizza costs $11.50 plus $0.75 per topping.

Therefore the cost of pizza with ‘x’ toppings is given as:

$11.50+0.75x$.

Angie and her sister have maximum $15 to spend on pizza. This means the price of pizza cannot exceed $15. Thus, the price of the pizza with toppings must be less than or equal to $15

Thus the required inequality is as follows:

$11.50+0.75x\le 15\dots \left(1\right)$

Step 3. Calculate the value of ‘x’.

Solve the inequality (1) to get the maximum number of toppings.

$11.50+0.75x\le 15$

Adding‘$-11.50$’ on both the sides of inequality

$$\begin{gathered} 11.50+0.75x-11.50\le 15-11.50 \\ 0.75x\le 3.50 \end{gathered}$$

Dividing throughout by 0.75

$$\begin{gathered} \frac{0.75x}{0.75}\le \frac{3.50}{0.75} \\ x\le 4.67 \end{gathered}$$

The number of toppings should be a whole number, less than and closest to 4.67 .

The whole number less than and closest to 4.67 is 4.

Thus Angie and her sister can get a maximum of 4 toppings.