Question

62.)
here is the ingredient list for the \best chocolate chip cookies\ recipe. the recipe
will produce around 36 cookies. you are hosting an \after mid - year exam party\
where you are planning on having 50 of your classmates to attend in order to relax
and unwind after a stressful week of mid - year exams. you calculate that each
person will have 3 cookies each. you must adjust the ingredient list accordingly so
that you have enough cookie batter to bake enough cookies for you and your
friends. what are the new amounts of each ingredient?

original recipe:

• 1 cup salted butter softened;
• 1 cup white (granulated) sugar
• 1 cup light brown sugar (packed)
• 2 tsp pure vanilla extract
• 2 large eggs
• 3 cups all - purpose (ap) flour
• 1 tsp baking soda
• 0.5 tsp baking powder
• 1 tsp sea salt
• 2 cups chocolate chips

__________ salted butter softened
__________ ap flour
__________ white granulated sugar
__________ baking soda

__________ light brown sugar
__________ baking powder

__________ pure vanilla extract
__________ sea salt

__________ eggs
__________ chocolate chips

Explanation:

Step1: Calculate total cookies needed

Total people = 50 (classmates) + 1 (yourself) = 51. Each person has 3 cookies, so total cookies = \( 51 \times 3 = 153 \).

Step2: Find the scaling factor

Original cookies = 36. Scaling factor \( k = \frac{153}{36} = \frac{17}{4} = 4.25 \).

Step3: Adjust each ingredient

• Salted butter: \( 1 \times \frac{17}{4} = \frac{17}{4} = 4.25 \) cups
• White granulated sugar: \( 1 \times \frac{17}{4} = 4.25 \) cups
• Light brown sugar: \( 1 \times \frac{17}{4} = 4.25 \) cups
• Pure vanilla extract: \( 2 \times \frac{17}{4} = \frac{17}{2} = 8.5 \) tsp
• Eggs: \( 2 \times \frac{17}{4} = \frac{17}{2} = 8.5 \) eggs (or 8 - 9 eggs, but we'll use the exact fraction for calculation)
• AP flour: \( 3 \times \frac{17}{4} = \frac{51}{4} = 12.75 \) cups
• Baking soda: \( 1 \times \frac{17}{4} = 4.25 \) tsp
• Baking powder: \( 0.5 \times \frac{17}{4} = \frac{17}{8} = 2.125 \) tsp
• Sea salt: \( 1 \times \frac{17}{4} = 4.25 \) tsp
• Chocolate chips: \( 2 \times \frac{17}{4} = \frac{17}{2} = 8.5 \) cups

Answer:

• Salted butter softened: \( \boldsymbol{4.25} \) cups
• White granulated sugar: \( \boldsymbol{4.25} \) cups
• Light brown sugar: \( \boldsymbol{4.25} \) cups
• Pure vanilla extract: \( \boldsymbol{8.5} \) tsp
• Eggs: \( \boldsymbol{8.5} \) (or 9) eggs
• AP flour: \( \boldsymbol{12.75} \) cups
• Baking soda: \( \boldsymbol{4.25} \) tsp
• Baking powder: \( \boldsymbol{2.125} \) tsp
• Sea salt: \( \boldsymbol{4.25} \) tsp
• Chocolate chips: \( \boldsymbol{8.5} \) cups