Question 1184410
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x-y-6=0  ==>  x = y+6<br>
Since x and y are both single-digit integers, there are only a few possibilities.  Solving the problem by trial and error is probably easier than solving it using formal algebra.<br>
y=0, x=6  ==>  he was born in 1960; his age in 1989 was 29; 1+9+6+0 is not equal to 29.  Doesn't work.<br>
y=1, x=7  ==>  he was born in 1971; his age in 1989 was 18; 1+9+7+1 = 18.  It works!<br>
So Gabe was born in  1971.<br>
ANSWER: Gabe's age in 1990 was 1990-1971 = 19<br>
It turns out that a solution using formal algebra is relatively easy....<br>
His age in 1989 is the difference between 89 and "xy", which algebraically is<br>
{{{89-(10x+y)=89-10x-y}}}<br>
His age in 1989 is equal to the sum of the digits of the year in which he was born:<br>
{{{89-10x-y=1+9+x+y}}}
{{{79=11x+2y}}}<br>
Given the restriction that x and y are both single digit positive integers, the only solution to that equation is x=7 and y=1.<br>
Of course you could finish that last step still using formal algebra, knowing that x=y+6:<br>
{{{79=11x+2y}}}
{{{79=11(y+6)+2y}}}
{{{79=11y+66+2y=13y+66}}}
{{{13=13y}}}
{{{y=1}}}
{{{x=y+6=7}}}<br>
So again (of course!) we find he was born in 1971, which means his age in 1990 was 19.<br>