Chapter 11.7, Problem 23PPE

a.

To determine

Write and graph an equation that gives the number of Calories C consumed by each person as a function of the total number of people n.

Answer to Problem 23PPE

  $\frac{1920}{n}+100=C$

  

Explanation of Solution

Given:

Nutrition for lunch, you bought two veggie pizzas for you and your friends to divide evenly. Each pizza contains 960 Calories. In addition, each person eats a banana, which contains 100 Calories.

Calculation:

Each pizza contains 960 Calories.

2 pizzas contain $960\cdot 2=1920$ Calories.

Each Banana contains 100 Calories.

Let total no. of people $=n$

Equation that gives the number of Calories C consumed by each person is as a function of the total number of people n.

  $\begin{array}{l}\frac{1920}{n}+100=C\\ whereC=Calories\\ n=totalno.ofpeople\end{array}$

b.

To determine

Approximately how many people must share the pizzas in order for each person to consume about 500 Calories?

Answer to Problem 23PPE

4 people

Explanation of Solution

Given:

Nutrition for lunch, you bought two veggie pizzas for you and your friends to divide evenly. Each pizza contains 960 Calories. In addition, each person eats a banana, which contains 100 Calories.

Calculation:

Each pizza contains 960 Calories.

2 pizzas contain $960\cdot 2=1920$ Calories

Banana contains 100 Calories

If each person consume about 500 Calories

No. of people must share the 2 pizzas

  $\begin{array}{c}\frac{1920}{n}+100=500\\ \frac{1920}{n}=500-100\\ \frac{1920}{n}=400\\ 1920=400n\\ n=\frac{1920}{400}\\ n=4.8\end{array}$

4 people can share 2 pizzas to consume 500 calories each.