A science

A science experiment calls for making 3 and 2/3 cups of distilled water with 1 and 3/5 cups of vinegar and 2/3 cups of liquid detergent. How much liquid in all cups is needed?

Correct answer:

x =  5 ¹⁴⁄₁₅ = 89/15

Step-by-step explanation:

$$\begin{gathered} w=3\frac{2}{3}=3+\frac{2}{3}=\frac{3\cdot 3+2}{3}=\frac{9+2}{3}=\frac{11}{3}=3\frac{2}{3}\doteq 3.6667 \\ v=1\frac{3}{5}=1+\frac{3}{5}=\frac{1\cdot 5+3}{5}=\frac{5+3}{5}=\frac{8}{5}=1\frac{3}{5}=1.6 \\ d=2/3=\frac{2}{3}\doteq 0.6667 \\ x=w+v+d=\frac{11}{3}+\frac{8}{5}+\frac{2}{3}=\frac{55}{15}+\frac{24}{15}+\frac{10}{15}=\frac{55+24+10}{15}=\frac{89}{15}=5\frac{14}{15}=5.9333 \end{gathered}$$

Try another example