A cookie recipe that makes 24 cookies call for the following ingredients: 2 3/4 c. Flour 1 1/3 c. Sugar.
3/4 c. Butter
1 egg 3 1/2 t. Baking powder 1 1/2 t. Vanilla extract
Amy is hosting a party and will have 16 people in attendance, including herself. She wants to make one large batch of cookies to accommodate everyone. If each person will eat three cookies, what are the new amounts that Amy must measure for each ingredient?
I’ve been trying to figure it out for a couple of days now! Thanks so much in advance.
1) How many cookies does she need?
$16$ people and $3$ cookies each is $16\times 3 = 48$ cookies.
2) How many cookies does one recipe make?
One recipe makes $24$ cookies.
3) If she makes $k$ recipes how many cookies does $k$ recipes make?
Each recipe makes $24$ cookies so $k$ recipes make $24 \times k$ cookies.
4) How many recipes must she make to make enough cookies?
$k$ recipes make $24\times k$ cookies. And she needs $48$ so you needs to make however many $k$ is so that $24 \times k = 48$.
So solve that:
$24 \times k = 48$ so
$24\times k \div 24 = 48 \div 24$
$k = 2$.
5) If she needs to make $2$ recipes worth what does she need to do to the ingrediant to make one recipe become $2$ recipes worth?
She must multiple every ingredient by $2$.
6) What are the new amounts when they are multiplied by $2$.
$2 \frac 34\times 2$ c. Flour
$1 \frac 13\times 2$ c. Sugar.
$\frac 34 \times 2$ c. Butter
$1\times 2$ egg
$3 \frac 12\times 2$ t. Baking powder
$1 \frac 12\times 2$ t. Vanilla extract
7) What are those values?
What is $2\frac 34 \times 2$?
a) Put the mixed fraction as an improper fraction:
$2 \frac 34 = 2 + \frac 34 = \frac 21 + \frac 34 = \frac 21\times \frac 44 + \frac 34 = \frac {2\times 4}4 + \frac 34 = \frac 84 + \frac 34 = \frac {8+3}4 = \frac {11}{4}$.
b) Multiple by $2$ by putting multiplying the numerator by $2$.
$\frac {11}4 \times 2 = \frac {11\times 2}{4}$.
!!!ADVICE!!!! Do NOT multiply $11 \times 2$ yet. Wait! You may have to cancel out common factors so there is no point multiplying yet if you will just have to divide out later!
c) Find any common factors between the numerator and the denominator.
Denominator $4= 2\times 2$ and the numerator $11\times 2 = 11 \times 2$. $11$ can't be broken any further.
So we have $\frac {11\times 2}{4} = \frac {11\times 2}{2\times 2}$
d) Cancel common factors
$\frac {11\times \color{red}2}{2\times\color{red}2}=\frac {11}2\times \frac {\color{red}2}{\color{red}2} = \frac {11}2\times \color{red}1 = \frac {11}2$.
e) Reduce to mixed fraction.
$\frac {11}2 = \frac {10+1}{2} = \frac {2\times 5 + 1}{2} = \frac {\color{red}2\times 5}{\color{red}2} + \frac 12 = 5+\frac 12 = 5\frac 12$.
f) You are done. $5\frac 12$ c.Flour
The rest:
$1\frac 13= \frac 33 + \frac 13 = \frac 43$.
$\frac 43 \times 2 = \frac {4\times 2}3 = \frac 83$.
$\frac 83 = \frac {6+2}3 = \frac {2\times 3 + 2}3 =\frac {2\times 3}3 + \frac 23=2+\frac 23 = 2\frac 23$
So $2\frac 23$ cups sugar.
$\frac 34\times 2 = \frac {3\times 2}{4} = \frac {3\times 2}{2\times 2} =\frac 32$
$\frac 32 = \frac {2 + 1}2 = \frac 22 + \frac 12 = 1\frac 12$ butter.
$1\times 2 = 2$ so $2$ eggs.
$3\frac 12 = 3+\frac 12 = \frac {3\times 2}2 + \frac 12 = \frac {2\times 3 +1}2 =\frac 72$.
$\frac 72 \times 2 = \frac {7\times 2}2 = 7$ so $7$ teaspoons baking powder. (Actually when you double a recipe you are only suppose to multiply the powder by one and a half....)
And $1\frac 12 \times 2 = 3$. (I'm tired of typing.)