The owner of a milk store finds that he can sell 980 litres of milk each week at Rs 14/liter and 1220 liters of milk each week at Rs 16/liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17/liter?
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Hint: For solving such a question, we are going to frame the above question in linear equations in two variables. We will find the equation of the straight line from the given condition. We will get the final result.
Complete step-by-step answer:
980 liters of milk each week at Rs 14/liter and 1220 liters of milk each week at Rs 16/liter. The relationship between selling price and demand is linear.
We have to find how many liters he could sell weekly at Rs 17/liter.
Let find the linear relations
Let us assume that the selling price/liter is along X-axis and demand along Y-axis.
Therefore, points (14, 980) and (16, 1220) satisfy the linear relationship between selling price and demand.
Hence, line passing through these points is:
\[
\Rightarrow y - 980 = \dfrac{{1220 - 980}}{{16 - 14}}\left( {x - 14} \right) \\
\Rightarrow y - 980 = \dfrac{{240}}{2}\left( {x - 14} \right) \\
\Rightarrow y - 980 = 120\left( {x - 14} \right) \\
\Rightarrow y = 120\left( {x - 14} \right) + 980 \\
\]
Put x = 17 in above equation, we get:
$
y = 120\left( {17 - 14} \right) + 980 \\
y = 120 \times 3 + 980 \\
y = 1340 \\
$
Hence, the owner of the milk store can sell 1340 liters of milk weekly at Rs 17/liter
Additional information: Linear equations in two variables If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax + by = r is called a linear equation in two variables. (The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax+by = r. The number r is called the constant of the equation ax + by = r.
Note: Linear equations in two variables have many methods to solve the equations. Such as
1. Graphical method
2. Elimination method
3. Substitution method
4. Cross multiplication method
Complete step-by-step answer:
980 liters of milk each week at Rs 14/liter and 1220 liters of milk each week at Rs 16/liter. The relationship between selling price and demand is linear.
We have to find how many liters he could sell weekly at Rs 17/liter.
Let find the linear relations
Let us assume that the selling price/liter is along X-axis and demand along Y-axis.
Therefore, points (14, 980) and (16, 1220) satisfy the linear relationship between selling price and demand.
Hence, line passing through these points is:
\[
\Rightarrow y - 980 = \dfrac{{1220 - 980}}{{16 - 14}}\left( {x - 14} \right) \\
\Rightarrow y - 980 = \dfrac{{240}}{2}\left( {x - 14} \right) \\
\Rightarrow y - 980 = 120\left( {x - 14} \right) \\
\Rightarrow y = 120\left( {x - 14} \right) + 980 \\
\]
Put x = 17 in above equation, we get:
$
y = 120\left( {17 - 14} \right) + 980 \\
y = 120 \times 3 + 980 \\
y = 1340 \\
$
Hence, the owner of the milk store can sell 1340 liters of milk weekly at Rs 17/liter
Additional information: Linear equations in two variables If a, b, and r are real numbers (and if a and b are not both equal to 0) then ax + by = r is called a linear equation in two variables. (The “two variables” are the x and the y.) The numbers a and b are called the coefficients of the equation ax+by = r. The number r is called the constant of the equation ax + by = r.
Note: Linear equations in two variables have many methods to solve the equations. Such as
1. Graphical method
2. Elimination method
3. Substitution method
4. Cross multiplication method