Word Problem Solution3





In this page word problem solution3 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:

(iii) A two digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.

Solution:

Let "x y" be the required two digit number

Here x is in the ten's digit place and y is in unit place. To form the first equation we have to consider this particular from the question that is a two digit number(xy) is seven times the sum of its digits

x y = 7 (x + y)

Now we have to write the two digit number (xy) in expanded form

10 x + 1 y = 7 x + 7 y

10 x - 7 x + 1 y - 7 y = 0

   3 x - 6 y = 0  ------ (1)

To form the second equation we have to consider this particular from the question that is The number formed by reversing the digits is 18 less than the given number.

y x = x y - 18

10 y + 1 x = 10 x + 1 y - 18

10 x - 1 x + 1 y - 10 y = 18

9 x - 9 y = 18

Divide the whole equation by 2 => x - y = 2  ----- (2)

Multiply the second equation by 6 we get

                       6 x – 6 y = 12

                       3 x - 6 y = 0

                       6 x – 6 y = 12

                     (-)    (+)     (-)

                     ------------------

                       - 3 x   = -12

                          x = (-12)/(-3)

                          x = 4

Now we have to apply the value of x in the first or second equation to get the value of y.

Substitute x = 4 in the first equation we get

3 x - 6 y = 0 

3(4) - 6 y = 0

12 - 6 y = 0

  -6 y = - 12

      y = (-12)/(-6)

      y = 2

Verification:

x – y = 2 

4 - 2 = 2

2 = 2

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