SOLUTION: A two digit number is such that its value equals four times the sum of its digits.If 27 is added to the number the results is equal to the value of the number obtained when the dig

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Question 1159944: A two digit number is such that its value equals four times the sum of its digits.If 27 is added to the number the results is equal to the value of the number obtained when the digits are interchanged.What is the number?
Found 2 solutions by math_helper, MathTherapy:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

N = the two-digit number = 10a + b (1)
We are told
4a+4b = N (2)
and
10a+b + 27 = 10b + a (3) (27 added to the number results in reversal of digits)

(1) and (2) can be used to eliminate N:
10a+b = 4a+4b
This simplfies to 6a-3b = 0
(3) simplifies to 9a-9b = -27
These last two equations can be solved easily for a=3, b=6 ==>
Check:
3(4)+6(4) = 12+24 = 36 (ok)
36 + 27 = 63 (digits reversed, ok)

Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!

A two digit number is such that its value equals four times the sum of its digits.If 27 is added to the number the results is equal to the value of the number obtained when the digits are interchanged.What is the number?
Let the tens and units digits be T, and U, respectively
Then we get: 10T + U = 4(T + U)
6T = 3U
2T = U ------ eq (i)

Also, 10T + U + 27 = 10U + T
10T - T + U - 10U = - 27
9T - 9U = - 27
9(T - U) = 9(- 3)
T - U = - 3 ------ eq (ii)

T - 2T = - 3 ------ Substituting 2T for U in eq (ii)
- T = - 3
Tens digit, or 
2(3) = U ------ Substituting 3 for T in eq (i)
Units digit or 
Number: 

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