Chapter 7.1, Problem 32P

A pizza shop makes large pizzas with a target diameter of 16 inches. A pizza is acceptable if its diameter is within $3\cdot 2^{-2}$ in. of the target diameter. Let $d$ represent the diameter of a pizza. Write an inequality for the range of acceptable large pizza diameters in inches.

To determine

To derive the inequality for the range of acceptable diameters of the pizzas in inches.

Answer to Problem 32P

  $\frac{61}{4}<d<\frac{67}{4}$

Explanation of Solution

Given: The target diameter of the pizza is 16 inches. A pizza is acceptable if its diameter is within $3·2^{-2}$ inches of the target diameter. An inequality is to be written for the ranges of diameters of the acceptable pizzas. Representing d as the diameter of the pizza.

Calculation:

Acceptable range of diameter of pizzas in inches,

  $\begin{array}{l}=16\pm 3·2^{-2}\\ =16\pm 3·\frac{1}{2^2}\\ =16\pm \frac{3}{4}\\ =\frac{64\pm 3}{4}\\ =\frac{67}{4},\frac{61}{4}\end{array}$

So, the acceptable range of pizzas $\frac{61}{4}<d<\frac{67}{4}$ . And this is the desired inequality.