Pack of cream

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

Final Answer:

x =  5.3333

Step-by-step explanation:

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

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