SOLUTION: Find the 2-digit number whose tens digit is 3 less than the units digit and the original number is 6 more than 4 times the sum of the digits.
Question 133849: Find the 2-digit number whose tens digit is 3 less than the units digit and the original number is 6 more than 4 times the sum of the digits. Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let x=the tens digit
And let y=the units digit
-----------tens digit is 3 less than the units digit
x=y-3----------------------------------------------------eq1
--------------original number is 6 more than 4 times the sum of the digits.
(10x+y)-6=4(x+y) simplify
10x+y-6=4x+4y subtract 4x and 4y from and add 6 to both sides
10x-4x+y-4y-6+6=4x-4x+4y-4y+6 collect like terms
6x-3y=6 divide both sides by 3
2x-y=2--------------------------------------eq2
substitute x=y-3 from eq1 into eq2
2(y-3)-y=2 or
2y-6-y=2 add 6 to both sides
2y-6+6-y=2+6 collect like terms
y=8-----------------------------------units digit
x=y-3=8-3=5------------------------------tens digit
CK
-------------------tens digit is 3 less than the units digit
8-5=3
3=3
--------------original number is 6 more than 4 times the sum of the digits
58=4(5+8)+6
58=52+6
58=58
