Diala

Diala bought some books in 2012, and then during 2013, she bought 3 times as many books as she bought in 2012. Diala bought 48 books during these two years.
Make a diagram to represent the given.
How many books did Diala buy each year?

Correct answer:

a =  12
b =  36

Step-by-step explanation:

$$\begin{gathered} b=3\cdot a \\ a+b=48 \\ 3a-b=0 \\ a+b=48 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 3a-b=0 \\ 1.33b=48 \\ b=\frac{48}{1.33333333}=36 \\ a=\frac{0+b}{3}=\frac{0+36}{3}=12 \\ a=12 \\ b=36 \end{gathered}$$

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