Two containers 2

Two containers, one large and one small, contain a total of 4 kilograms of bath salts. One-quarter of the bath salts from the large container are transferred to the small container, so the ratio of bath salts in the large container to that in the small one becomes 3:2. How many Kilograms of bath salts were originally in each container?

Correct answer:

a =  3.2 kg
b =  0.8 kg

Step-by-step explanation:

$$\begin{gathered} a+b=4kg \\ a-a/4:(b+a/4)=3:2 \\ a+b=4 \\ 2\cdot (\frac{3}{4}\cdot a)=3\cdot (b+\frac{a}{4}) \\ a+b=4 \\ 2\cdot (3/4\cdot a)=3\cdot (b+a/4) \\ a+b=4 \\ 3a-12b=0 \\ Pivot:Row1\leftrightarrow Row2 \\ 3a-12b=0 \\ a+b=4 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 3a-12b=0 \\ 5b=4 \\ b=\frac{4}{5}=0.8 \\ a=\frac{0+12b}{3}=\frac{0+12\cdot 0.8}{3}=3.2=3.2\text{kg} \\ a=\frac{16}{5}=3.2 \\ b=\frac{4}{5}=0.8 \end{gathered}$$

$$\begin{gathered} \text{ Verifying Solution: } \\ A=a-a/4=3.2-3.2/4=\frac{12}{5}=2.4\text{kg} \\ B=b+a/4=0.8+3.2/4=\frac{8}{5}=1.6\text{kg} \\ {r}_2=A:B=2.4:1.6=\frac{3}{2}=1.5=3:2 \\ b=0.8=0.8\text{kg} \end{gathered}$$

Try another example