SOLUTION: "I am a 4-digit odd number where the sum of my digits Is 22. the difference between my first digit and my last digit is equal to my third digit. my second digit is twice my third d

Algebra ->  Functions -> SOLUTION: "I am a 4-digit odd number where the sum of my digits Is 22. the difference between my first digit and my last digit is equal to my third digit. my second digit is twice my third d      Log On


   

Question 1058185: "I am a 4-digit odd number where the sum of my digits Is 22. the difference between my first digit and my last digit is equal to my third digit. my second digit is twice my third digit. My first digit is the domain value of f(x)=9x+3 if it's corresponding range value is 66." What's my number?
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The first digit is 7, which makes f(7)=66.
The last digit is x
The third digit is (7-x)
The second digit is (14-2x)
These add to 22
so, 7+7-x+14-2x+x=22
28-2x=22
x=3
The digits are 7843

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
"I am a 4-digit odd number where the sum of my digits Is 22. 
a = first digit
b = second digit
c = third digit
d = fourth (last) digit

a + b + c + d = 22 and d is odd
the difference between my first digit and my last digit
is equal to my third digit. 
a - d = c
my second digit is twice my third digit.
b = 2c
My first digit is the domain value of f(x)=9x+3 if
its corresponding range value is 66."
We find the value of x for which f(x) = 66 by setting

f(x) = 66
9x+3 = 66
  9x = 63
   x = 7

So the domain value for the range value of 66 is 7
Therefore the first digit = a = 7

The information so far is:

(1)   a + b + c + d = 22 and d is odd

(2)   a - d = c

(3)   b = 2c

(4)   a = 7

Substituting 7 for a in (1) and (2)

(1)   a + b + c + d = 22 and d is odd
      7 + b + c + d = 22 and d is odd
(5)       b + c + d = 15 and d is odd

(2)   7 - d = c
          7 = c + d
(6)   c + d = 7

Subtracting (6) from (5):

(5)       b + c + d = 15 and d is odd
(6)           c + d =  7
------------------------
          b         =  8

Substituting 8 for b in (3)

(3)   b = 2c
      8 = 2c
      4 = c

Substituting 4 for c in (6)

(6)   c + d = 7
      4 + d = 7
          d = 3   <-- yes, d is odd.

So now we have a=7, n=8, c=4, d=3
What's my number?
7843

Edwin