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

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

Step 1 :- Understand the Problem

• Let the score of Zoe be 'x'.

• Let the score of Yesha be 'y'.

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Step : 2 Devise a plan

• The sum of scores of Zoe and Yesha is atleast 12.

$\boxed{ \blue{ \: \rm : \implies \:x \: + \: y \: \geqslant \: 12}} \: - - (i)$

• The difference of their scores is more than 3.

$\boxed{ \blue{ \: \rm : \implies \:x \: - \: y \: > \: 3}} - - (ii)$

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Step :- 3 Carry out the plan

Let us consider (i),

$\rm : \implies \:x \: + \: y \: = \: 12$

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 12 \\ \\ \sf 6 & \sf 6 \\ \\ \sf 12 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the above points.

Now,

Let us consider,

$\rm : \implies \:x \: - \: y \: = \: 3$

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 3 \\ \\ \sf 4 & \sf 1 \\ \\ \sf 3 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

➢ See the attachment graph.

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Step :- 4 Look back

Let us choose any point from the solution set say (10, 5)

• Now, we have to check this point

$\rm : \implies \:x + y \geqslant 12$

$\rm : \implies \:10 + 5 \geqslant 12$

$\rm : \implies \:15 \geqslant 12$

Also,

$\rm : \implies \:x - y > 3$

$\rm : \implies \:15 - 10 > 3$

$\rm : \implies \:5 > 3$

Answer 2

Step-by-step explanation:

Polya's method:-

Step-1:-

Understanding the problem:-

Let X be the score of Zoe

and Y be the score of Yesha.

Step -2:-

Devise a plan:-

X+Y≥12 ------(1)

X-Y>3 --------(2)

Step-3:-

Carryout the plan:-

Y ≥ -X+12

Y> -X+3

Step-4:-

Look back:-

(15,10)

15+10≥12

25≥12

15-10>3

5>3