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

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) (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) (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 be the tens digit, and be the units digit. The the first condition says and the second condition says .
Substitute the first equation into the second and get Rearrange to get so and so
Hope that helps.
Kev
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