A shopkeeper 5

A shopkeeper sold some sets of Pencils and Pens. Each set contained 6 pencils and 2 pens. If the shopkeeper sold 112 pencils and pens, how many pens did she sell altogether?

Correct answer:

a =  28

Step-by-step explanation:

$$\begin{gathered} a:b=2:6 \\ a+b=112 \\ a+b=112 \\ 6a=2b \\ a+b=112 \\ 6\cdot a=2\cdot b \\ a+b=112 \\ 6a-2b=0 \\ Pivot:Row1\leftrightarrow Row2 \\ 6a-2b=0 \\ a+b=112 \\ Row2-\frac{1}{6}\cdot Row1\to Row2 \\ 6a-2b=0 \\ 1.33b=112 \\ b=\frac{112}{1.33333333}=84 \\ a=\frac{0+2b}{6}=\frac{0+2\cdot 84}{6}=28 \\ a=28 \\ b=84 \end{gathered}$$

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