SOLUTION: Please help me with this problem: Find the two-digit number whose tens digit is 3 less than the units digit. The original number is 6 more than 4 times the sum of the digits. I c

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Question 25804: Please help me with this problem:
Find the two-digit number whose tens digit is 3 less than the units digit. The original number is 6 more than 4 times the sum of the digits.
I could REALLY use your HELP!
Found 2 solutions by atif.muhammad, kev82:
Answer by atif.muhammad(135) About Me  (Show Source):
You can put this solution on YOUR website!
Each two digit number has two numbers (duh!).
Let's allow the tens digit to be x and the units digit to be y.
Tens digit is 3 less than the units digit: x = y-3
Original number is 6 more than 4 times the sum of the digits: 10x+y-6 = 4x + 4y
This gives us simulataneous equations!
First let's clear the mess:
1. x= y-3
2. 6x-3y=6
Substitute 1 into 2:
6(y-3) -3y =6
6y - 18 - 3y = 6
3y = 24
y = 8
Our units digit is 8
Substitute y= 8 into 1.
x = y - 3
x = 5
Our tens digit is 5
Therefore, our number is 58.
Let's test this.
Tens digit is 3 less than units digit: 58 --> 5 is 3 less than 8!
Original number is 6 more than 4 times the sum of the digits --> sum of the digits = 13, 4 times the sum of the digits = 52, Add 6, 58!
We have proven that our number is 58!

Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
You can solve this with algebra if you want, but I don't think it's worth the effort. We know the number must be two digits, and that the tens digit is 3 less than the units digit. So that means the number must be one of
14
25
36
47
58
69
The number also has to be 6 more than 4 times the sum of it's digits, so lets work out 4*(sum digits)+6 for each of these numbers
14 : 26
25 : 34
36 : 42
47 : 50
58 : 58 - Ah Ha!
69 : 66
As you can see 58 is the answer. If you are interested in the algebraic solution then let t be the tens digit, and u be the units digit. The the first condition says t=u-3 and the second condition says 10t%2Bu=4%28t%2Bu%29%2B6.
Substitute the first equation into the second and get 11u-30=8u-6 Rearrange to get 3u=24 so u=8 and t=u-3 so t=5
Hope that helps.
Kev