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Question
The owner of a milk store finds that he can sell 980 litres milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.
Solution
Let x denote the price per litre and y denote the quantity of the milk sold at this price.
Since there is a linear relationship between the price and the quantity, the line representing this relationship passes through (14, 980) and (16, 1220).
So, the equation of the line passing through these points is
\[y - 980 = \frac{1220 - 980}{16 - 14}\left( x - 14 \right)\]
\[ \Rightarrow y - 980 = 120\left( x - 14 \right)\]
\[ \Rightarrow 120x - y - 700 = 0\]
When x = 17 then we have,
\[120 \times 17 - y - 700 = 0\]
\[ \Rightarrow y = 1340\]
Hence, the owner of the milk store can sell 1340 litres of milk at Rs 17 per litre.
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