college problem solving
posted by luckybee .
a certain twodigit number is 6 less than the sum of its tens digit and 7 times its units digit. if the digits are reversed the number is increase by 27. fin the original twodigit numbers

let the tens digit be x and the unit digit be y
then the number is 10x + y
10x+y = (x+7y)  6
9x  6y = 6
3x  2y = 2 , #1
the number reversed would be 10y + x
so 10y+x = 10x+y + 27
9x  9y = 27
3x  3y = 9 , #2
#1  #2
y = 7
then from #1, x = 4
the number is 47
check:
reverse it  74
is 74 47 = 27 , so far so good
what is the sum of its tens digit and 7 times its unit digit
4 + 7(7) = 53
is 53 greater than 47 by 6 ? YEAHHHH
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