# The owner of a milk store finds that he can sell $980$ litres of milk each week at $Rs14$ per litre and $1220$ litres of milk each week at $Rs16$ per litre. Assuming a linear relationship between selling price and demand, how many litres could you sell weekly at $Rs17$ per litre?

Last updated date: 18th Mar 2023

•

Total views: 306k

•

Views today: 4.86k

Answer

Verified

306k+ views

**Hint:**Assume one of the entities to be along x axis and the other to be along y axis. We have 2 points on the graph where each point has one x value and one y value, using these points form an equation of line and then put the value of the asked entity in the equation to obtain the answer.

**Complete step by step answer:**

Selling price be along the $x$–axis.

And demand for milk is along the $y$–axis.

Let, $y$ litre be sold at Rs.$x/litre$

Considering the given statement, the owner sells $980$ litres milk at Rs $14/litre$.

Let,

${x_1} = 14,{y_1} = 980$

And the next case is owner sells $1220$ litres of milk each week at $Rs16$ per litre,

Therefore,

${x_2} = 16,{y_2} = 1220$

Equation of line passing through $\left( {14,980} \right)$ and $\left( {16,1220} \right)$ .

So, on using the line formula, we have,

$\left( {y - 980} \right) = \dfrac{{1220 - 980}}{{16 - 14}}\left( {x - 14} \right)$

$\left( {y - 980} \right) = \dfrac{{240}}{2}\left( {x - 14} \right)$

$\left( {y - 980} \right) = 120\left( {x - 14} \right)$

$y = 120\left( {x - 14} \right) + 980$

Now, in the question they have asked us to find the milk that can be sold at the rate of $Rs17/litre$.

Therefore, on equating $x = 17$, we get,

$y = 120\left( {x - 14} \right) + 980$

$y = 120\left( {17 - 14} \right) + 980$

$y = 120 \times 3 + 980$

$y = 360 + 980$

$y = 1340$

**Therefore, $1340$ litres of milk can be sold at the rate of $Rs17/litre$.**

**In this question, we took selling price on x-axis and demand on y-axis and then took the values of both to plot the graph, in this graph we have 2 points using these points we formed equation of line and then finally equated x=17 in the equation to get the result.**

Note:

Note:

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE