Birthday

Brano received money from his uncle for his birthday. When he went to the store, he counted out loud: "If I buy chocolates for 1 euro and 30 cents each, I will have 60 cents left. But if I wanted to buy the same number of chocolates for 1 euro and 40 cents each, I would be 20 cents short."
a) How many chocolates did Brano want to buy?
b) How much money did Brano receive from his uncle?

Final Answer:

a =  8
b =  11 Eur

Step-by-step explanation:

$$\begin{gathered} 1.30a=b-0.60 \\ 1.40a=b+0.20 \\ 1.30\cdot a=b-0.60 \\ 1.40\cdot a=b+0.20 \\ 1.3a-b=-0.6 \\ 1.4a-b=0.2 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1.3}{1.4}\cdot Row1\to Row2 \\ -0.07b=-0.79 \\ b=\frac{-0.78571429}{-0.07142857}=11 \\ a=\frac{0.2+b}{1.4}=\frac{0.2+11}{1.4}=8 \\ a=8 \\ b=11 \end{gathered}$$

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