SOLUTION: A 2 digit numberis 6 less than 4 times the sum of its digits. If digits are interchange, the new number is 5 less than 8 times the sum of its digits. What's the original number?

Question 92711: A 2 digit numberis 6 less than 4 times the sum of its digits. If digits are interchange, the new number is 5 less than 8 times the sum of its digits. What's the original number?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A 2 digit numberis 6 less than 4 times the sum of its digits. If digits are interchange, the new number is 5 less than 8 times the sum of its digits. What's the original number?
--------------
Comment: Any two digit number can be written as 10t+u where t is the ten's
digit and u is the unit's digit.
------------------
EQUATIONS:
10t+u+6 = 4(t+u)
10u+t+5 = 8(t+u)
---------------------
Simplify each equation to get:
6t-3u=-6
7t-2u= 5
-------------
Multiply thru the 1st by 2; Multiply thru the 2nd by 3
----------
12t-6u = -12
21t-6u = 15
---------------
Subtract the 1st from the 2nd to get:
9t = 27
t = 3
-----------
Substitute into 6t-3u=-6 to solve for u:
18 - 3u = -6
3u = 24
u = 8
---------------
the original number is 38
================================
Cheers,
Stan H.

RELATED QUESTIONS
A 2 digit number is 3 more than 7 times the sum of its digits. If the digits are... (answered by ankor@dixie-net.com)

.a two-digit number is three less than seven times the sum of two digits.if the digits... (answered by stanbon)

A 2-digit number is one more than 6 times the sum of its digits. If the digits are... (answered by richwmiller)

A 2-digit number is one more than 6 times the sum of its digits. If the digits are... (answered by josgarithmetic,greenestamps)

the tens digit of a three-digit number is 3 less than 5 times the unit digit. three times (answered by ankor@dixie-net.com)

A number consists of two digits sum of its digit is 15. if the place of digits are... (answered by josmiceli,addingup,Theo)

1)The sum of the digits is 6. The number is 6 times its units digit. 2) The sum of the (answered by solver91311)

A two-digit number is three less than seven times the sum of its digits. If the digits... (answered by 24HoursTutor.com)

A two Digit number is three less than seven times the sum of its digits if the digits are (answered by mananth)