Pack of cream

A mother uses one pack of cream in 12 weeks, and a daughter in 14 weeks. They used the cream together for four weeks, then only the daughter used it. How many more weeks did her cream last?

Correct answer:

x =  5.3333

Step-by-step explanation:

$$\begin{gathered} a=12 \\ b=14 \\ t=\frac{1}{a}+\frac{1}{b}=\frac{1}{12}+\frac{1}{14}=\frac{7}{84}+\frac{6}{84}=\frac{7+6}{84}=\frac{13}{84}\doteq 0.1548 \\ 4\cdot t+x\cdot \frac{1}{b}=1 \\ 4\cdot t+x/b=1 \\ 4\cdot b\cdot t+x=1\cdot b \\ x=b-4\cdot b\cdot t \\ x=b\cdot (1-4\cdot t)=14\cdot (1-4\cdot 0.1548)=5.3333 \end{gathered}$$

Try another example