Your chocolate

Your chocolate chip cookie recipe makes three dozen cookies, but you need four dozen cookies. If the recipe requires 1 7/8 cups of vegetable oil, 2 1/2 teaspoons of almond extract, and 3 1/2 cups of oatmeal, how many of these ingredients are necessary for four dozen cookies? Simplify your answer.

Correct answer:

v₄ =  2 ¹⁄₂ = 5/2
a₄ =  3 ¹⁄₃ = 10/3
o₄ =  4 ²⁄₃ = 14/3

Step-by-step explanation:

$$\begin{gathered} k=\frac{4}{3}\doteq 1.3333 \\ {v}_3=1\frac{7}{8}=1+\frac{7}{8}=\frac{1\cdot 8+7}{8}=\frac{8+7}{8}=\frac{15}{8}=1\frac{7}{8}=1.875 \\ {v}_4=k\cdot v_3=\frac{4}{3}\cdot \frac{15}{8}=\frac{4\cdot 15}{3\cdot 8}=\frac{60}{24}=\frac{5}{2}=2\frac{1}{2}=2.5 \end{gathered}$$

$$\begin{gathered} a_3=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2\frac{1}{2}=2.5 \\ {a}_4=k\cdot a_3=\frac{4}{3}\cdot \frac{5}{2}=\frac{4\cdot 5}{3\cdot 2}=\frac{20}{6}=\frac{10}{3}=3\frac{1}{3}=3.3333 \end{gathered}$$

$$\begin{gathered} o_3=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3\frac{1}{2}=3.5 \\ {o}_4=k\cdot o_3=\frac{4}{3}\cdot \frac{7}{2}=\frac{4\cdot 7}{3\cdot 2}=\frac{28}{6}=\frac{14}{3}=4\frac{2}{3}=4.6667 \end{gathered}$$

Try another example