Candies

The price for 1 kg of more expensive candies is 125 CZK.
The price for 1 kg of cheaper candy is 100 CZK.
We mix two different mixtures of candy.

A) The first mixture contains 2 kg more expensive and 0.5 kg cheaper candy. Calculate the price for 1 kg of the mixture.
B) The second mixture contains 2 kg of more expensive candy and several kg of cheaper candy. The price per 1 kg of this mix is 110 CZK. Calculate how many kilos of cheaper candy contains the second mixture.

Correct answer:

A =  120 Kc/kg
B =  3 kg

Step-by-step explanation:

$$\begin{gathered} a=125 \\ b=100 \\ A=(2\cdot a+0.5\cdot b)/(2+0.5)=(2\cdot 125+0.5\cdot 100)/(2+0.5)=120\text{Kc/kg} \end{gathered}$$

$$\begin{gathered} 2\cdot a+B\cdot b=110\cdot (2+B) \\ 2\cdot 125+B\cdot 100=110\cdot (2+B) \\ 10B=30 \\ B=\frac{30}{10}=3 \\ B=3=3\text{kg} \end{gathered}$$

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