SOLUTION: The sum of the digits of a two-digit number is 5. If the number is multiplied by 3 and 1 is taken from the result, the digits are reversed. Find the number.

Algebra ->  Radicals -> SOLUTION: The sum of the digits of a two-digit number is 5. If the number is multiplied by 3 and 1 is taken from the result, the digits are reversed. Find the number.       Log On


   

Question 1112782: The sum of the digits of a two-digit number is 5. If the number is multiplied by 3 and 1 is taken from the result, the digits are reversed. Find the number.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the tens digit and y be the one's digit
:
1) x +y = 5
:
2) 3(10x +y) - 1 = 10y +x
:
solve equation 1 for y
:
y = 5 -x
:
substitute for y in equation 2
:
3(10x +5 -x) -1 = 10(5 -x) +x
:
30x +15 -3x -1 = 50 -10x +x
:
27x +14 = 50 -9x
:
36x = 36
:
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x = 1
y = 5 -1 = 4
:
the number is 14
:
check the answer
:
3(14) -1 = 42 -1 = 41
:
answer checks
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