SOLUTION: The sum of the digits of a two-digit number is 14. When the digits are reversed, the resulting number is 23 less than two times the original number. What is the original number?

Question 417381: The sum of the digits of a two-digit number is 14. When the digits are reversed, the resulting number is 23 less than two times the original number. What is the original number?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x-- ten's digit
y --- unit's digit
x+y =14........1
10y+x= 2(10x+y)-23
10y+x=20x+2y-23
8y-19x=-23............2
x+y=14 .............1
-19x+8y= -23.............2

multiply (1)by -8
Multiply (2) by 1
-8x-8y=-112
-19x+8y= -23

Add the two equations
-27x=-135

/-27

x=5

plug value of x in (1)
x+y=14
5+y=14
y=14-5
y=9
Number is 59
y = 9

RELATED QUESTIONS
The sum of the digits of a two- digit number is 14. If the digits are reversed, the... (answered by josgarithmetic)

the sum of the digits of a two digit number is 9, when the digits are reversed the new... (answered by mananth)

The sum of the digits in a two-digit number is 8. When the digits are reversed, the new... (answered by london maths tutor)

2 LINEAR EQUATIONS IN 2 UNKNOWNS or SIMULTANEOUS LINEAR EQUATIONS IN 2 UKNOWNS The sum (answered by rothauserc)

The sum of the digits of a two-digit number is 14. If the digits are reversed, the new... (answered by josgarithmetic)

A two digit number, whose sum of digits is ten, will be 36 less than the original number... (answered by lwsshak3)

URGENT HELP: The sum of the digits of a two-digit number is 9. If the digits are... (answered by fcabanski)

When the digits of a two digit number are reversed, the resulting number is 54 less than... (answered by josgarithmetic,MathTherapy,ikleyn)

the value of a certain two digit number is four less than six times the sum of its... (answered by I<3Math123)