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Chi Y. asked • 07/27/18
The sum of the digits of a 2-digit number is 14. If it’s digit are reversed, the original number is increased by 18. What is the number?
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Andy C. answered • 07/27/18
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Math/Physics Tutor
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Here is the algebraic solution:
T is the tens digit
O is the ones digit
T+O = 14
So O = 14 - T <---- this is the first equation
The original number is 10*T + O
If the digits are reversed the original number is increased by 18.
The number if the digits are reversed is:
10*O + T = 10*T + O + 18
10*(14-T) + T = 10*T + (14-T) + 18 <--- substitutes O with 14-T per first equation above in bold
140 - 10T + T = 10T + 14 - T + 18 <--- distributive left side
140 - 9T = 9T + 32
140 = 9T + 9T + 32
140 - 32 = 9T + 9T
108 = 18T
108/18 = T
T= 6
THe tens digit is 6.
The ones digit must be 8.
Reversing 86 - 68 = 18
The original number is 68.
