SOLUTION: The tens-digit of a three digit number is 3 less than 5 times the units digit. Three times the sum of the digits is 2 more than 4 times the hundreds digit. If the digits are revers

Question 253285: The tens-digit of a three digit number is 3 less than 5 times the units digit. Three times the sum of the digits is 2 more than 4 times the hundreds digit. If the digits are reversed, the new number is 594 less than the original number. Find the original number. (find a system of 3 equations then use the system to find the original number).
Found 3 solutions by josmiceli, richwmiller, JimboP1977:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = hundreds digit
Let = tens digit
Let = units digit
The actual number must be

given:
(1)
(2)
The number with the digits reversed would be

(3)
-------------------------------------
I have the 3 equations and I just need to tidy them up
and solve for ,, and
I'll leave this for you
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Why do we need three equations? We need three equations because we will have three unknowns. We need one equation for each unknown.
Let the digits be h, t and u
Let the number be 100h+10t+u
t=5u-3
3*(h+t+u)=2+4h
100u+10t+h+594=100h+10t+u
721
h=7
t=2
u=1
check
2=5*1-3
2=5-3=2 ok
3*(7+2+1)=2+4*7
3*10=2+28
30=30 ok
127+594=721
721=721 ok
Answer by JimboP1977(311)   (Show Source): You can put this solution on YOUR website!
Let H be the hundreds digit
Let T be the tens digit
Let U be the units digit.
We are given the following:
(1)
(2)
(3)
Rearrange (1) to equal T. Then substitute into (2).

(4)
Collect terms in (3) to give (5)
Subsitute (4) into (5) to give

Plug this result into (1) and (4) to give and
So the original number 781.
Does that make any sense?

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