SOLUTION: Twice the sum of the digits of a two-digit number is 14. The original number subtracted from the number formed when the digits are reversed is 27. What is the original number?

Question 1169114: Twice the sum of the digits of a two-digit number is 14. The original number subtracted from the number formed when the digits are reversed is 27. What is the original number?
Found 3 solutions by ankor@dixie-net.com, greenestamps, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
let the two digits be a & b
then
10a + b = the original number
:
Twice the sum of the digits of a two-digit number is 14.
2(a+b) = 14
simplify divide by 2
a + b = 7
The original number subtracted from the number formed when the digits are reversed is 27.
(10b + a) - (10a + b) = 27
10b - b + a - 10a = 27
9b - 9a = 27
simplify divide by 9
b - a = 3
:
Use elimination with these two equations
a + b = 7
-a + b = 3
---------------Addition eliminates a, find b
0 + 2b = 10
b = 10/2
b = 5
then
a + 5 = 7
a = 7 - 5
a = 2
:
What is the original number? 25
:
:
Confirm this in the statement:
"The original number subtracted from the number formed when the digits are reversed is 27."
52 - 25 = 27
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

If twice the sum of the digits is 14, then the sum of the digits is 7.

If the original number subtracted from the number with the digits reversed is 27, then the difference between the digits is 27/9 = 3.

Sum of the two digits = 7 and difference of the two digits = 3 means the digits are 5 and 2.

ANSWER: 52

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Twice the sum of the digits of a two-digit number is 14. The original number subtracted from the number formed when the digits are reversed is 27. What is the original number?

Correct answer: Since the original number, when SUBTRACTED from the reversed number, is 27, it's obvious that the reversed number will be LARGER than the original number. Therefore, the original number CANNOT be 52. Twice the sum of the 2 digits is 24, so sum of the 2 digits is 7. Let tens digit be T Then U (units digit) = 7 - T Original number: 10T + U Reversed number: 10U + T We then get: 10U + T - (10T + U) = 27 10U + T - 10T - U = 27 9U - 9T = 27_____9(U - T) = 9(3)_____U - T = 3 ----- eq (i) 7 - T - T = 3 ------ Substituting 7 - T for U in eq (i) - T - T = 3 - 7 - 2T = - 4 Tens digit or Units digit: 7 - 2, or 5

RELATED QUESTIONS
The sum of the digits of a certain two digit number is 5. If the number formed by... (answered by mathstutor458)
The sum of the digits of a certain two digit number is eight. If the original number is... (answered by mathstutor458,josmiceli,lwsshak3)
The sum of the digits if a certain two digit number is 6. If the original number is... (answered by Alan3354)
The sum of the digits of a certain two digit number is 10. If the number formed by... (answered by Alan3354)
The sum of the digits of a two-digit number is 14. If 36 is subtracted from the number,... (answered by mananth)
the sum of the digits of a two digit number is 14. if the number represented by reversing (answered by arunpaul)
THE SUM OF THE DIGITS OF A TWO-DIGIT NUMBER IS 14. IF THE NUMBER REPRESENTED BY... (answered by solver91311)
A number consists of two digit whose sum is 9. the Number formed by revising the digits... (answered by josgarithmetic)
The sum of the digits of a two digit number is 14. If 36 is subtracted from the number,... (answered by oberobic)