Chapter 6.2, Problem 20PPS

To determine

To find the sugar needed to make $4\frac{1}{2}$ dozen cookies.

Answer to Problem 20PPS

Hence $1\frac{11}{16}$ cups of sugar is needed to make $4\frac{1}{2}$ dozen cookies.

Explanation of Solution

Given:

2 dozen cookies need $\frac{3}{4}$ cup sugar.

Calculation:

According to given data, we have

  $\begin{array}{l}2\text{dozen}\text{cookies}=\frac{3}{4}\text{cup}\text{of}\text{sugar}\\ \Rightarrow 1\text{dozen}\text{cookies}=\frac{\frac{3}{4}}{2}\text{cup}\text{of}\text{sugar}\\ \Rightarrow 1\text{dozen}\text{cookies}=\frac{3}{8}\text{cup}\text{of}\text{sugar}\\ \Rightarrow 4\frac{1}{2}\text{dozen}\text{cookies}=\frac{3}{8}\times 4\frac{1}{2}\text{cups}\text{of}\text{sugar}\\ \Rightarrow 4\frac{1}{2}\text{dozen}\text{cookies}=\frac{3}{8}\times \frac{9}{2}\text{cups}\text{of}\text{sugar}\\ \Rightarrow 4\frac{1}{2}\text{dozen}\text{cookies}=\frac{27}{16}\text{cups}\text{of}\text{sugar}\\ \Rightarrow 4\frac{1}{2}\text{dozen}\text{cookies}=1\frac{11}{16}\text{cups}\text{of}\text{sugar}\end{array}$

Hence $1\frac{11}{16}$ cups of sugar is needed to make $4\frac{1}{2}$ dozen cookies.