algebra fraction

Question

A two digit number is 4/7 of the number formed by reversing its digits.When the number is increased by 2 times the sum of its digits,it becomes 54.find the number.

 

Answer 1

Let the digits be x and y. So the original number must be 10x +y because the left digit is in the tens column.

 

10x + y = 4/7(10y + x) 

 

If you distribute, combine like terms, and reduce, you get 2x = y  (1)

 

Also, 10x +y + 2(x + y) = 54   Again, if you distribute, combine like terms, and reduce, you get  y = 18 - 4x  (2)

 

Combining (1) and (2), you get 2x = 18 - 4x, so x = 3, and from (1), y = 6 

 

THE ORIGINAL NUMBER IS THEREFORE 36