From peanuts

From peanuts priced at 160 CZK/kg and almonds priced at 200 CZK/kg, 20 kg of a nut mixture priced at 190 CZK/kg is to be prepared. The price of the mixture is determined by the ratio in which the nuts are mixed.
a) Determine how many kilograms of each type of nut need to be mixed.
b) Determine the price of one kilogram of the mixture if the price of almonds increases by 10 CZK/kg.

Final Answer:

a =  5 kg
m =  15 kg
b =  197.5 Kc/kg

Step-by-step explanation:

$$\begin{gathered} w=20\text{kg} \\ 160a+200m=w\cdot 190 \\ a+m=w \\ 160a+200m=20\cdot 190 \\ a+m=20 \\ 160\cdot a+200\cdot m=20\cdot 190 \\ a+m=20 \\ 160a+200m=3800 \\ Row2-\frac{1}{160}\cdot Row1\to Row2 \\ -0.25m=-3.75 \\ m=\frac{-3.75}{-0.25}=15 \\ a=\frac{3800-200m}{160}=\frac{3800-200\cdot 15}{160}=5=5\text{kg} \\ a=5 \\ m=15 \end{gathered}$$

$b=\frac{160\cdot a+210\cdot m}{w}=\frac{160\cdot 5+210\cdot 15}{20}=\frac{395}{2}\text{Kc/kg}=197.5\text{Kc/kg}$

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