SOLUTION: A two-digit counting number has a value that is 7 times the sum of its digits. If 5 times the units' digit is 9 more than the tens' digit, what is the number.

Question 82514: A two-digit counting number has a value that is 7 times the sum of its digits. If 5 times the units' digit is 9 more than the tens' digit, what is the number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
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