Question 66687
a two-digit number is twice the sum of its digit.  If the tens digit is 7 less than the unit digit, find the number.

Let x= the unit digit
Then y= the tens digit
And 10y+x= the number



x+y= the sum of the digits

Now we are told that 10y+x=2(x+y)  ------1st equation

We are also told that y=x-7  ----------- 2nd Equation

So our equations to solve are:

(1)  10y+x=2(x+y)
(2)   y=x-7 


Substitute (2) into (1)

10(x-7)+x=2(x+x-7)  simplifying we have

10x-70+x=2x+2x-14  Collecting like terms:

11x-70=4x-14  subtract 4x from both sides and add 70 to both sides:

11x-4x=70-14
7x=56
x=8  the unit digit

Substite x=8 in (2):
y=x-7=8-7;
y=1 the tens digit

The 2 digit number is 10+8=18

ck

y=x-7
1=8-7=1
1=1
18=2(8+1)
18=18

Hope this helps ----ptaylor