Answer
423.9k+ views
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
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)