Question

A cookie recipe calls for 7/6 of a cup of flour and makes 3 dozen cookies. If Cassandra plans to make 21 dozen cookies, how many cups of flour does she need?Cassandra needs ____ cup(s) of flour.(Simplify your answer.)

Answer 1

Given that:

- The recipe calls for this amount of flour for 3 dozen cookies:

$\frac{7}{6}cup$

- Cassandra plans to make 21 dozen​ cookies.

Let be "x" the number of cups of flour she needs to make 21 dozen​ cookies.

Using the data given in the exercise, you can set up the following proportion:

$\frac{\frac{7}{6}}{3}=\frac{x}{21}$

Now you have to solve for "x":

1. You can rewrite the expression on the left side as follows:

$\frac{7}{6}\cdot\frac{1}{3}=\frac{x}{21}$

2. Simplify by multiplying the fractions on the left side:

$\frac{7}{18}=\frac{x}{21}$

3. Multiply both sides of the equation by 21:

$\begin{gathered} \frac{7}{18}\cdot21=\frac{x}{21}\cdot21 \\ \\ \frac{147}{18}=x \end{gathered}$

4. You can reduce the fraction by dividing the numerator and the denominator by 3:

$\begin{gathered} \frac{147\div3}{18\div3}=x \\ \\ x=\frac{49}{6} \end{gathered}$

Hence, the answer is:

$\frac{49}{6}cups$