SOLUTION: the sum of the digits of a two-digit number is 13. the value of the number is 2 more than 7 times the units digit.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the sum of the digits of a two-digit number is 13. the value of the number is 2 more than 7 times the units digit.      Log On


   

Question 418999: the sum of the digits of a two-digit number is 13. the value of the number is 2 more than 7 times the units digit.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tens digit = a
Let the units digit = b
given:
(1) a+%2B+b+=+13
(2) 10a+%2B++b+=+7b+%2B+2
-----------------
(2) 10a+-+6b+=+2
Multiply both sides of (1) by 6
and add the equations
(2) 10a+-+6b+=+2
(1) 6a+%2B+6b+=+78
+16a+=+80+
a+=+5
and, since
a+%2B+b+=+13
b+=+13+-+5
b+=+8
The number is 58
check:
(2) 10a+%2B++b+=+7b+%2B+2
10%2A5+%2B+8+=+7%2A8+%2B+2
58+=+58
OK