Question

A cookie recipe requires $\frac{3}{4}\text{cup}$ of flour and $\frac{1}{3}\text{cup}$ of butter to make one batch of cookies.

Wendy has $2\text{cups}$ of flour and $\frac{3}{4}\text{cup}$ of butter.

What is the greatest number of batches she can make?

Answer 1

Step-1. Find the number of batches that can be made from available flour:

It is given that each batch of cookies require $\frac{3}{4}\text{cup}$ of flour and Wendy has $2\text{cups}$ of flour.

The number of batches that can be made using $2\text{cups}$ of flour is

$\begin{array}{rcl}2÷\frac{3}{4}& =& 2\times \frac{4}{3}\\ & =& \frac{8}{3}\\ & =& 2+\frac{2}{3}\end{array}$

Thus $2\text{cups}$ of flour is enough for $2\text{complete batches}$ of cookies with $\frac{2}{3}\text{cup}$ of flour remaining unused.

Note that only the integer part of the quotient is used because cookies are to be made in complete batches only.

Step-2: Find the number of batches that can be made from available butter.

It is given that each batch of cookies require $\frac{1}{3}\text{cup}$ of butter and Wendy has $\frac{3}{4}\text{cup}$ of butter.

The number of batches that can be made using $\frac{3}{4}\text{cup}$ of butter is

$\begin{array}{rcl}\frac{3}{4}÷\frac{1}{3}& =& \frac{3}{4}\times \frac{3}{1}\\ & =& \frac{9}{4}\\ & =& 2+\frac{1}{4}\end{array}$

Thus $\frac{3}{4}\text{cup}$ of butter is enough for $2\text{complete batches}$ of cookies with $\frac{1}{4}\text{cup}$ of butter remaining unused.

Note that only the integer part of the quotient is used because cookies are to be made in complete batches only.

Step-3: Find the number of batches that can be made from available flour and butter.

Thus, as many as $2\text{batches}$ of the cookies can be made from available flour.

Also, as many as $2\text{batches}$ of the cookies can be made from available butter.

Thus, Wendy can make as many as $2\text{batches}$ of cookies using the available ingredients.

Hence, Wendy can make as many as $\mathbf{2}\mathbf{}\mathbf{\text{batches}}$ of cookies using the available ingredients.