Question 180016
Find the two-digit number whose tens digit is 4 less than its units digit
 if the original number is 2 more than 3 times the sum of the digits.
:
Let x = 10s digit
Let y - units digit
:
10x + y = the number
:
the two-digit number whose tens digit is 4 less than its units digit"
x = y - 4
:
"the original number is 2 more than 3 times the sum of the digits."
10x + y = 3(x+y) + 2
10x + y = 3x + 3y + 2
10x - 3x = 3y - y + 2
7x = 2y + 2
Replace x with (y-4), find y
7(y-4) = 2y + 2
7y - 28 = 2y + 2
7y - 2y = 2 + 28
5y = 30
y = 6
then
x = 6 - 4
x = 2
:
The original number: 26
:
:
Check solution in the statement:
"the original number is 2 more than 3 times the sum of the digits."
26 = 3(2+6) + 2
26 = 3(8) + 2; confirms our solution