SOLUTION: What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second?

Question 996701: What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
What is the four-digit number
a, b, c, d
in which the first digit is one-third the second,
a = b
:
the third is the sum of the first and second,
c = a + b
replace a with b
c = b + b
c = b
Because we must have single digit integer solution, only two are possible
b=3 then c=4, and b=6, then c=8
:
and the last is three times the second?
d = 3b
From this we know that b is 3 or less to be single digit
therefore, from the last two statements:
b = 3, resulting in c=4
and
a = (3) = 1
and
d = 3(3) = 9
:
Our number: 1349

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second?

Let 1^st digit be F
Then 2^nd digit is: 3F
Also, 3^rd digit is: F + 3F, or 4F
And, 4^th digit is: 3(3F), or 9F
It's obvious, based on the above clues - especially the fact that the 4^th digit is: 9F - that F can only be 0 or 1, and since it cannot be 0, it MUST be 1
From there, we now know that the:
4^th digit is: 9(1), or 9
2^nd digit is: 3(1), or 3
3^rd digit is: 4(1), or 4
4-digit number:
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