Question

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Answer 1

$\large\underline\purple{\bold{Solution :- }}$

☆ Let number of munckin be 'x' and number of yema be 'y'

☆ According to first condition, we get

$\tt \longrightarrow \: x + y \geqslant 10 - - - (1)$

☆ According to second condition, we get

$\tt \longrightarrow \: 3x + 2y \geqslant 50 - - - (2)$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation (1) are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 10 \\ \\ \sf 5 & \sf 5 \\ \\ \sf 10 & \sf 0 \end{array}} \\ \end{gathered}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation (2) are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 25 \\ \\ \sf 10 & \sf 10 \\ \\ \sf 20 & \sf - 5 \end{array}} \\ \end{gathered}$

☆ Origin test for the first equation :-

$\tt \longrightarrow \: 0 + 0 \geqslant 10$

$\tt\implies \:0 \geqslant 10 \: false \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt \: so \: shade \: away \: from \: origin$

☆ Origin test for the second equation:-

$\tt \longrightarrow \: 3 \times 0 + 2 \times 0 \geqslant 50$

$\tt\implies \:0 \geqslant 50 \: false \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tt \: so \: shade \: away \: from \: origin$

Answer 2

Step-by-step explanation:

Steps in Polya's method:-

• Understanding the problem
• Devise a plan
• Carryout a plan
• Look back

Understanding the problem:-

Let x be the number of munchkin

y be the number of yemma

Devise a plan:-

x+y≥10----(1)

3x+2y≥50----(2)

Carryout a plan:-

y≥-x+10

and

y≥ -3/2 x + 25

Look back:-

(10,15)

10+15≥10

25≥10

and

3(10)+2(15)≥50

=>30+30≥50

60≥50