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The tens digit is two less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.

Respuesta :

let the number be xy then we have the following system of equations:-

y - x = 2....................................................(1)
10x+y + 10y + x = 154
11x + 11y = 154     Divide thru by 11:-

x + y = 14..................................................(2)

Add equation (1) AND (2):-

2y = 16

y = 8  
and x = 8-2 = 6


So your required number is 68.
fichoh

The value of the original number obtained using a system of linear equations is 68

Let the two digit number = ab

  • Tens digit = a
  • Unit digit = b

We can create the system of equations as follows :

b - a = 2 - - - - - - - - - - - - (1)

(10b + a) + (10a + b) = 154

10b + a + 10a + b = 154

11b + 11a = 154 - - - - - - - - - (2)

From (1) :

b = 2 + a ----- (3)

Substitute b = 2 + a into (2)

11(2 + a) + 11a = 154

22 + 11a + 11a = 154

22 + 22a = 154

22a = 154 - 22

22a = 132

a = 132 / 22

a = 6

From (3) :

b = 2 + 6

b = 8

Therefore, the original number, ab = 68

Learn more : https://brainly.com/question/18796573

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