Problem B and Solution

Baking Cookies

Felix and Vera are baking cookies. Their recipe bakes \(12\) cookies and uses the following ingredients:

\(\frac{1}{2}\) cup of butter

\(\frac{1}{3}\) cup of sugar

\(1\) cup of flour

\(\frac{2}{3}\) teaspoon of vanilla

Felix and Vera decide to triple the recipe. How much of each ingredient will they need?

The cookies are so good that Felix and Vera plan to make \(60\) cookies for a fundraiser.

How much butter will they need?

Each batch of cookies takes \(11\) minutes to bake, and their oven can fit only \(24\) cookies at a time. How long will it take to bake all the cookies for the fundraiser?

If they triple the recipe, then the amounts of each ingredient will be as follows:

Butter: \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{3}{2}=1 \frac{1}{2}\) cups

Sugar: \(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1\) cup

Flour: \(1+1+1=3\) cups

Vanilla: \(\frac{2}{3}+\frac{2}{3}+\frac{2}{3}=\frac{6}{3}=2\) teaspoons

Since \(12 \times 5 = 60\), they will need to make \(5\) batches of cookies. So the amount of butter they will need is \(5 \times \frac{1}{2} = \frac{5}{2} = 2\frac{1}{2}\) cups.

Their oven can fit only \(24\) cookies at a time, which is the same as \(2\) batches. Since they need to make \(5\) batches, they will need to bake \(2\) batches, then another \(2\) batches, then \(1\) batch. So the total baking time would be \(11+11+11=33\) minutes.