Question

read the instructions first
Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:
Step 1: Understand the problem.
Step 2: Devise a plan (translate).
Step 3: Carry out the plan (solve).
Step 4: Look back (check and interpret​

Answer 1

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

$\purple{\underline{\bold{Step : 1 \: \: Understand \: the \: Problem}}}$

• Let number of Avocado fruit be 'x'.

• Let the number of melon fruit be 'y'.

$\green{\underline{\bold{Step : 2 \: \: Devise \: a \: plan}}}$

According to statement,

• The number of avocado fruit is no more than thrice the melon

$\boxed{ \purple{\rm : \implies \:x \: \leqslant \: 3y \: }} - - (i)$

According to second condition,

• Total number of fruit is atleast 20.

$\boxed{ \purple{\rm : \implies \:x \: + \: y \: \geqslant \: 20}} - - (ii)$

$\blue{\underline{\bold{Step : \: 3 \: Carry \: out \: the \: plan }}}$

• Let us consider (i), we have

$\boxed{ \blue{\rm : \implies \:x \: = \: 3y \: }}$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0 \\ \\ \sf 10 & \sf 30 \\ \\ \sf 20 & \sf 60 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

Now,

• Let consider the (ii), we have

$\boxed{ \green{\rm : \implies \:x \: + \: y \: = \: 20 }}$

Hᴇɴᴄᴇ,

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

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

➢ Now draw a graph using the points

➢ Now, see the graph in attachment

$\pink{\underline{\bold{Step : \: 4 \: \: Look \: back \: (check \: and \: interpret)}}}$

Let us choose a coordinate (10, 20) from the solution set, we have

Consider,

$\rm : \implies \:x \: \leqslant \: 3y$

$\rm : \implies \:10 \leqslant 60$

Now,

Consider,

$\rm : \implies \:x \: + \: y \: \geqslant \: 20$

$\rm : \implies \:10 + 20 \geqslant 20$

$\rm : \implies \:30 \geqslant 20$

Answer 2

Step-by-step explanation:

Polya's method:-

Step - 1:-

a) Understanding the problem:-

Let the number of avocados be X

Let the number of melon be Y

b)Devise the plan:-

X≤3Y ----(1)

X+Y≥20 -----(2)

c) Carryout the plan:-

Y≥X/3

and

Y≥ -X+20

d) Look back:-

(15,15)

15≤3(15)

15≤45

and

15+15≥20

30≥20

Things to remember:-

There are 4 steps in Polya's method

They are

Step 1: Understand the problem.

Step 2: Devise a plan (translate).

Step 3: Carry out the plan (solve).

Step 4: Look back (check and interpret