Question

read the instructions first​

Answer 1

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

Step :- 1 Understand the Problem

• Let present age of Grace be 'x' years

• Let present age of Grace son be 'y' years

Step :- 2 Devise the plan

• Grace is more than 20 years old when her first son was born.

$\boxed{ \blue{ \: \rm : \implies \:x \: > \: 20}} - - (i)$

Also,

• Sum of their ages is no less than 60 years.

$\boxed{ \blue{ \: \rm : \implies \:x + y \geqslant 60}} - - (ii)$

Step :- 3 Carry out the plan

• Let us consider (i).

$\rm : \implies \:x \: = \: 20$

So, its a line parallel to y - axis, passes through (20, 0).

• Let us consider (ii).

$\rm : \implies \:x \: + \: y \: = \: 60$

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

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

➢ Now draw a graph using the points

➢ See the attachment graph.

Step :- 4 Look back and check and interpret

Let us choose coordinate (41, 21) from the solution set.

Now,

$\rm : \implies \:x > 20$

$\rm : \implies \:41 > 20$

Now,

$\rm : \implies \:x + y \geqslant 60$

$\rm : \implies \:41 + 21 \geqslant 60$

$\rm : \implies \:62 \geqslant 60$

Answer 2

Step-by-step explanation:

Polya's method:-

Step -1:-

a) Understanding the problem:-

Let the present age of Grace be Y years

Then her son's age be X years

b)Devise the plan:-

Y>X+20

X+Y≥60

c)Carry out the plan:-

Y>X+20

Y≥ -X+60

d) Look back:-

Consider (15,55)

55>15+20

55>35

and

15+55≥60

=>70≥60

Things to remember:-

There are 4 steps in Polya's method. they are

1. Understanding the problem
2. Devise the plan
3. Carry out the plan
4. Look back