Purchased 82877

Mrs. Havelková bought 7 kg of apples and 4 kg of pears for CZK 295. According to the receipt, she found out that 6 kg of apples and 5 kg of pears could be bought at the same cost. Determine the price of 1 kg of purchased apples and 1 kg of purchased pears.

Correct answer:

a =  25 Kc/kg
b =  30 Kc/kg

Step-by-step explanation:

$$\begin{gathered} 7a+4b=295 \\ 6a=5b \\ 7\cdot a+4\cdot b=295 \\ 6\cdot a=5\cdot b \\ 7a+4b=295 \\ 6a-5b=0 \\ Row2-\frac{6}{7}\cdot Row1\to Row2 \\ 7a+4b=295 \\ -8.43b=-252.86 \\ b=\frac{-252.85714286}{-8.42857143}=30 \\ a=\frac{295-4b}{7}=\frac{295-4\cdot 30}{7}=25=25\text{Kc/kg} \\ a=25 \\ b=30 \end{gathered}$$

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