Question 82514
Let x = the 10's digit; let y = the units digt
:
A two-digit counting number has a value that is 7 times the sum of its digits.
 10x + y = 7(x + y)
 10x + y = 7x + 7y
 10x - 7x = 7y - y
  3x = 6y
   x = 2y: divided both sides by 3
:
 If 5 times the units' digit is 9 more than the tens' digit, what is the number.
   5y = x + 9
Substitute 2y for x and find y
   5y = 2y + 9
   5y - 2y = 9
    3y = 9
     y = 9/3
     y = 3 is the units digit
:
Find x: 
x = 2y
x = 2(3)
x = 6
:
The two digit number is 63
:
Check: Does the number = 7 times the sum of the digits?
 63 = 7(6+3), yes it does