The sum of the digits of a two - digit number is 8. The value of the number is 2 less than 11 times the tens digit. Find the number

Guest Feb 22, 2015

#2**+8 **

Let x be the "10s" digit and y be the "1s" digit and the value of the number is 10x + y

"The sum of the digits = 8" implies x + y = 8 which implies that y = 8 - x

"The value of the number is 2 less than 10 times the 10s digit" implies 10x + y + 2 = 11x

So...subbing in y = 8 - x into the second equation, we have

10x + (8 - x) + 2 = 11x simplify

9x + 10 = 11x subtract 9x from both sides

10 = 2x so x = 5 y = 8 - 5 = 3

So..the number is 53....!!!

CPhill
Feb 22, 2015

#1**+8 **

Answer: 53

1. Assign each digit a variable, let's call the 10's digit x, and the 1's digit y.

2. Set up a system of equations.

The first equation is the simplest, it is that (x + y = 8)

The second is tougher, The value of the number in terms of x and y is (10x + y). Assume the digits are 1 and 2, if x = 1 and y = 2 then we know the number is 12, but 1 + 2 is not 12, it is 3. In order to get 12 we must multiply the 10's digit (x) by 10 and add the y digit, since it is a 2 digit number. If it was a 3 digit number then the 100's digit would be multiplied by 100 and so on.

So now this gives us the second equation (10x + y = 11x - 2) the second part comes from the fact that the number is 11 times the 10's digit minus 2.

Now use substitution, from the first equation we get that (x = 8 - y). If we substitute this in for all the x's in the 2nd equation, and simplify we would get (80 - 9y = 86 - 11y). Simplify again and we get (2y = 6).

**Now you can do the rest.**

Guest Feb 22, 2015

#2**+8 **

Best Answer

Let x be the "10s" digit and y be the "1s" digit and the value of the number is 10x + y

"The sum of the digits = 8" implies x + y = 8 which implies that y = 8 - x

"The value of the number is 2 less than 10 times the 10s digit" implies 10x + y + 2 = 11x

So...subbing in y = 8 - x into the second equation, we have

10x + (8 - x) + 2 = 11x simplify

9x + 10 = 11x subtract 9x from both sides

10 = 2x so x = 5 y = 8 - 5 = 3

So..the number is 53....!!!

CPhill
Feb 22, 2015