Strawberries - shop

Mom and grandma went shopping at the market. Mom bought 2 kg of strawberries and 3 liters of blueberries and paid 250 CZK. Grandma bought 1 kg more strawberries and 0.5 l fewer blueberries than mom and paid 45 CZK more than her. How much did 1 kg of strawberries and 1 liter of blueberries cost?

Correct answer:

a =  65 Kc/kg
b =  40 Kc/l

Step-by-step explanation:

$$\begin{gathered} 2\cdot a+3\cdot b=250 \\ (2+1)\cdot a+(3-0.5)\cdot b=45+250 \\ 2a+3b=250 \\ 3a+2.5b=295 \\ Pivot:Row1\leftrightarrow Row2 \\ 3a+2.5b=295 \\ 2a+3b=250 \\ Row2-\frac{2}{3}\cdot Row1\to Row2 \\ 3a+2.5b=295 \\ 1.33b=53.33 \\ b=\frac{53.33333333}{1.33333333}=40 \\ a=\frac{295-2.5b}{3}=\frac{295-2.5\cdot 40}{3}=65=65\text{Kc/kg} \\ a=65 \\ b=40 \end{gathered}$$

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