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Question
The owner of a milk store finds that he can sell 980 litres of milk each week at ₹ 14/litre and 1220 litres of milk each week at ₹ 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at ₹ 17/litre?
Solution
Let the selling price of a milk be “x”
Let the demand be “y”
We have to find the linear equation connecting them
Two points on the line are (14, 980) and (16, 1220)
Slope of the line = `(y_2 - y_1)/(x_2 - x_1)`
= `(1220 - 980)/(16 - 14)`
= `240/2`
= 120
Equation of the line is y – y1 = m (x – x1)
y – 980 = 120(x – 14)
⇒ y – 980 = 120x – 1680
– 120x + y = – 1680 + 980
⇒ – 120x + y = – 700
⇒ 120x – y = 700
Given the value of x = 17
120(17) – y = 700
– y = 700 – 2040
⇒ – y = – 1340
y = 1340
The demand is 1340 liters
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