SOLUTION: i am a 4 digit number the ratio of my first digit to my second digit is 3 to 1 the ratio of my thrid digit to my last digit is 1 to 3 the ratio of my first digit to my last is 2 to

Question 409475: i am a 4 digit number the ratio of my first digit to my second digit is 3 to 1 the ratio of my thrid digit to my last digit is 1 to 3 the ratio of my first digit to my last is 2 to 3 if all my diit add up to 20 what number am i
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement:
:
i am a 4 digit number
a, b, c, d
;
the ratio of my first digit to my second digit is 3 to 1
=
cross multiply
a = 3b
:
the ratio of my third digit to my last digit is 1 to 3
=
d = 3c
:
the ratio of my first digit to my last is 2 to 3
=
2d = 3a
3a - 2d = 0; we will use this later in elimination.
:
all my digits add up to 20, what number?
a + b + c + d = 20
replace a with 3b, and replace d with 3c
3b + b + c + 3c = 20
4b + 4c = 20
Divide by 4
b + c = 5
therefore:
a + d = 20 - 5
a + d = 15
Use eliminations multiply the above by 2, add to this equation
3a - 2d = 0
2a + 2d = 30
--------------adding eliminates d, finda
5a = 30
a = 30/5
a = 6
then
6 + d = 15
d = 9
and
d = 3c
9 = 3c
c = 3
:
Find b:
b = 20 - 6 - 3 - 9
b = 2
:
The number 6239

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