The sum of a two digit number and another formed by reversing its digits is 99 . Five added to the number yields 4 less than 6 times the sum of its digits. Find the number.
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10x+y+10y+x=99
11x+11y=99
x+y=9
10x+y+5=6(x+y)-4
10x+y+5=6x+6y-4
4x-5y=-9
x=9-y
4(9-y)-5y=-9
36-4y-5y=-9
9y=45
y=5
x=4
The number is 45.
11x+11y=99
x+y=9
10x+y+5=6(x+y)-4
10x+y+5=6x+6y-4
4x-5y=-9
x=9-y
4(9-y)-5y=-9
36-4y-5y=-9
9y=45
y=5
x=4
The number is 45.
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