Question

There are instructions written near the arrow in the following diagram.

Answer 1

x+y=36
2x-y=27
x-y=6
y=(5/7)x

Answer 2

Given :

Some instructions are given near the arrow in the diagram.

To Find :

The value of Length and width of the rectangle.

Explanation :

The equations are as following from the given instructions :

x + y = 36 .......(i)

$y=\frac{5}{7}x$     ........(ii)

x - y = 6 ..........(iii)

2x - y = 27 ......(iv)

1. From equation (i) and (ii) :

Putting the value of y from equation (ii) in equation (i)

$x+\frac{5}{7}x=36$

$\frac{7x+5x}{7}=36$

$\frac{12x}{7}=36$

$x=\frac{36\times 7}{12}$

x = 21

Put the value of x in equation (i)

21 + y = 36

y = 36 - 21

y = 15

2.  From equation (i) and (iii)

x + y = 36 ....(i)

x - y = 6 ........(iii)

add both the equations

2x = 42

x = $\frac{42}{2}$

x = 21

Put the value of x in equation (i)

21 + y = 36

y = 36 - 21

y = 15

3. From equation (i) and (iv)

x + y = 36 ........(i)

2x - y = 27 .......(iv)

add both the equations

3x = 63

$x=\frac{63}{3}$

x = 21

Now Put the value of x in equation (i)

21 + y = 36

y = 36 - 21

y = 15

4. From equation (ii) and (iii)

$y=\frac{5}{7}x$ ........(ii)

x - y = 6 ......(iii)

Put the value of y from equation (ii) in equation (iii)

$x-\frac{5}{7}x=6$

$\frac{7x-5x}{7}=6$

$\frac{2x}{7}=7$

$x=\frac{6\times 7}{2}$

x = 21

Now Put the value of x in equation (iii)

21 - y = 6

y = 21 - 6

y = 15

5. From equation (ii) and (iv)

$y=\frac{5}{7}x$ ..........(ii)

2x - y = 27 ......(iv)

Put the value of y from equation (ii) in equation (iv)

$2x-\frac{5}{7}x=27$

$\frac{14x-5x}{7}=27$

9x = 27 × 7

$x=\frac{27\times 7}{9}$

x = 21

Now Put the value of x in equation (iv)

2x - y = 27

y = 2(21)- 27

y = 42 -27

y = 15

6. From equation (iii) and (iv)

x - y = 6 ......(iii)

2x - y = 27 .......(iv)

Subtract equation (iii) from equation (iv)

2x - y = 27

x - y = 6

x = 21

Now Put the value of x in equation (iii)

21 - y = 6

y = 21 - 6

y = 15

There are total 6 pairs can be formed.