Word Problem Solution5





In this page word problem solution5 we are going to see solution for first word problem of the worksheet cross multiplication method.

Formulate the following problems as a pair of equations,and hence find their solutions:

(ii) In a rectangle,if the length is increased and breadth is reduced each by 2 cm then the area is reduced by 28 cm². If the length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm². Find the area of the rectangle.

Solution:

Let x be the length of the rectangle

Let y be the breadth of the rectangle

Area of the rectangle = x y

length is increased and breadth is decreased by 2, so that the area is reduced by 28 cm²

(x + 2) (y -2) = x y - 28

x y - 2 x + 2 y - 4 = x y - 28

2 x - 2 y = 28 - 4 

2 x - 2 y = 24

Divide the whole equation by 2 we get

 x - y = 12 ----- (1)

to form the second equation we have to consider the given information from the question that is length is reduced by 1 cm and the breadth is increased by 2 cm,then the area increases by 33cm².

(x-1) (y+2) = x y + 33

x y + 2 x - y - 2 = x y + 33

2 x - y + x y - x y = 33 + 2

2 x - y = 35 ----- (2)

                        x - y = 12

                       2 x - y = 35

                     (-)   (+)   (-)

                     --------------

                         -x   = -23

                          x = 23

Substitute x = 23 in the first equation we get

x - y = 12

23 - y = 12

    - y = 12 - 23

   - y= - 11

      y = 11

Therefore the length of the rectangle = 23 cm

Breadth of the rectangle = 11 cm

Verification:

x – y = 12 

23 - 11= 12

12 = 12

word problem solution5  word problem solution5


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