Question

Raj and Ranjan each has certain no.of chocolates.raj says to Ranjan ,if you give me 6 of your chocolates, I will have twice the no.of chocolates left of you .Ranjan replies,if you give me 4 of your chocolates, I will have the same no.of chocolates as left with you . represent the situation algebraically and graphically.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

Raj has 'x' chocolates

and

Ranjan has 'y' chocolates

So,

According to statement,

Raj says to Ranjan ,if you give me 6 of your chocolates, I will have twice the no.of chocolates left of you .

$\rm :\longmapsto\:x + 6 = 2(y - 6)$

$\rm :\longmapsto\:x + 6 = 2y - 12$

$\rm :\longmapsto\:x - 2y = - 12 - 6$

$\bf :\longmapsto\:x - 2y = - 18 - - - (1)$

According to statement again,

Ranjan replies to Raj, if you give me 4 of your chocolates, I will have the same no.of chocolates as left with you.

$\rm :\longmapsto\:y + 4 = x - 4$

$\bf :\longmapsto\:x - y = 8 - - - (2)$

Consider Equation (1),

$\bf :\longmapsto\:x - 2y = - 18$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 - 2y = - 18$

$\rm :\longmapsto\:- 2y = - 18$

$\rm :\longmapsto\:y =9$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:x - 2(0) = - 18$

$\rm :\longmapsto\:x = - 18$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 9 \\ \\ \sf - 18 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 9) & (- 18 , 0)

➢ See the attachment graph.

Consider Equation (2),

$\bf :\longmapsto\:x - y = 8$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 - y = 8$

$\rm :\longmapsto\:y = - 8$

Substituting 'y = 0' in the given equation, we get

$\rm :\longmapsto\:x - 0 = 8$

$\rm :\longmapsto\:x= 8$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 8 \\ \\ \sf 8 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 8) & (8 , 0)

➢ See the attachment graph.

From graph, we concluded that x = 34 and y = 26.

Hence,

• Raj has 34 chocolates

• Ranjan has 26 chocolates.