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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.
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! 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
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